Engineering

This is LambdaGeeks Mechanical Engineering vertical, which includes all the posts related to Mechanical Engineering and Thermal Engineering.

How To Calculate Relative Humidity: From Different Entities And Facts

Relative Humidity(RH) measurement plays a crucial role in different fields. How to calculate Relative Humidity” is the main concern of this article.

To calculate Relative Humidity we use different devices and methods. Many applications like air conditioning systems, food storage, weather forecasting, wood drying process, cooling tower, etc. require regular monitoring of relative humidity.

Relative Humidity Measuring Device; Image Credit: Pixabay

In simple words, relative humidity is the ratio of the current amount of water vapor in the air to the maximum capacity of holding water vapor by the air at a particular temperature.

Relative Humidity has changed along with the change in temperature.

The Relative Humidity can be expressed as follows:

Relative Humidity(%)= \frac{Actual Vapor Density}{Saturation Vapor Density}X100%

The relative humidity is always expressed in percentage(%).

If the Relative Humidity is 50% that means the air holds a half of the water vapor it can theoretically hold.

Generally, a psychrometer or hygrometer containing both wet-bulb and dry-bulb thermometers is used as RH measuring device.

How to calculate Relative humidity with Wet Bulb and Dry Bulb?

Relative humidity can be calculated from the difference between the temperature on the wet-bulb thermometer and on the dry-bulb thermometer and using a relative humidity chart.

Using two thermometers (dry bulb and wet bulb) we can determine the Relative Humidity at our home or an area and can know if too much or too little moisture in it. The Relative humidity percentage has a great difference at various temperatures because warmer air holds more moisture than cooler air.

Wet Bulb Thermometer; Image Credit: Wikipedia

The steps followed to calculate the Relative Humidity with Wet Bulb and Dry Bulb thermometer as follows:

Take two bulb thermometers side by side and wrap a water soaked cloth on one of the two thermometers.

After some time, observe the temperature reading of both the thermometers and note down the readings in degrees Fahrenheit or degrees Celsius.

The dry thermometer gives air temperature which is true thermodynamic temperature. The temperature reading obtained from the wet-bulb is the lowest one due to evaporation from the wetted surface.

Since the wet-bulb temperature reading is less than the dry-bulb temperature, we will subtract  T_{wb} from T_{db} to get the difference.

Now using the psychrometric chart we can calculate the RH.

how to calculate relative humidity
Psychrometric Chart; Image Credit: Wikipedia

How to Calculate Humidity in a Room?

We know the Relative Humidity in a room, we can use a device called hygrometer. Over the centuries these instruments has changed, advanced and different types as per the user’s requirement.

The main use of hygrometer is to measure the amount of water vapor in air, apart from that it has numerous commercial uses. Now a days as per the requirement or applications different varieties of hygrometers are available in the market.

An excessive amount of moisture content in the air creates molds and pollutants inside the houses while not an adequate amount results in skin irritation, breathing-related problems, electrostatic discharge, etc. To maintain a proper humidity level we can use dehumidifiers or vaporizers to adjust the environmental humidity manually.

Hygrometer; Image Credit: Wikipedia

How to Calculate Relative Humidity with Temperature?

Relative Humidity indicates the percentage of moisture present in comparison to the maximum amount of moisture in the air at a specific temperature.

The Relative Humidity is higher at a lower temperature because cold air can hold more water vapors than warm air. The RH is temperature specific and tends to change with temperature changes too.

Relative Humidity is inversely proportional to the temperature for a fixed amount of water vapor.

The Relative Humidity can be expressed as follows:

Relative Humidity(%)=\frac{Actual Vapor Pressure}{Saturation Vapor Pressure}X100% Eq(1)

As the denominator value in equation(1) increases, the RH value obtained is decreased.

Therefore when saturated water vapor pressure decreases (with temperature decrement), related humidity value increases until air gets saturated.

How to Calculate Relative Humidity from Humidity?

Humidity refers to the amount of water vapor present in the air.

In general, we can say humidity is measured in three different ways: Relative, Absolute, and Specific Humidity which indicate moisture content in the air in three different ways.

The Relative Humidity can be expressed as follows:

Relative Humidity(%)= \frac{Actual Vapor Density}{Saturation Vapor Density}X100%

How to Calculate Relative Humidity using a Sling Psychrometer?

Sling Psychrometers are a type of battery-free hygrometer, most widely used for certain characteristics like inexpensive, easy to use, low maintenance, portable, etc.

Steps followed to measure the Relative Humidity are as follows:

  • Take off the reservoir cap of the psychrometer and fill the reservoir with water.
  • Fill the reservoir with water to make the wick saturated, tightly secure the lid of the chamber. Similarly, make sure that the wick at the end portion of the thermometer must be wet.
  • Keep the mercury reservoir in the dry-bulb thermometer dry.
  • Now in the area where we have to measure the Relative Humidity, swing the psychrometer speedily in the air for a minute or two.
  • Stop whirling the psychrometer to stabilize the temperatures, note down the readings from both the thermometers.
  • Now calculate the wet-bulb depression value by subtracting wet bulb temperature from dry bulb temperature.
  • With the help of the attached table or psychromatic chart determine RH value. For that locate the dry bulb temperature on the horizontal axis of the chart, and then mark the wet bulb depression value on the vertical axis.
  • Now mark the intersection point of the two readings to obtain the Relative Humidity value in percentage.
  • For more accuracy repeat the method for two /three times.
Sling Psychrometers; Image Credit: Flickr

A large difference between the dry and wet bulb temperature indicates low RH value and on the contrary a small difference is indicating towards higher RH value. If the dry and wet bulb temperatures are equal then we can say Relative Humidity is 100%.

How to calculate Relative Humidity with Temperature and Vapor pressure?

Saturated vapor pressure increases with increasing temperature, therefore Relative Humidity decreases with increasing temperature.

The Relative Humidity can be expressed as follows:

Relative Humidity(%)= \frac{Actual Vapor pressure}{Saturation Vapor pressure}X100%

How to Calculate Relative Humidity with Temperature and Dew Point?

Dew point is the temperature at which air must be cooled for saturation to occur (dew to form)and to reach100% Relative Humidity.

The steps followed to calculate RH using known temperature and dew point are described below:

  • The temperature of air and dew point must be in Celsius, if not then convert to degree Celsius.
  • We can convert Fahrenheit into Celsius using the formula

               C=\frac{5}{9}(F-32)   Eq(1)

               where C= Celsius temperature, F= Fahrenheit temperature,

  • Now calculate the Saturated Vapor Pressure(E_{s}) using the formula

                E_{s}=6.11\cdot\exp{\frac{7.5T}{273.3+T}} Eq(2)

                where T=Air Temperature, E_{s}=Standard Vapor Pressure

  • Now determine the Actual Vapor Pressure(E) using the same formula i.e Eq(2)

                E=6.11\cdot\exp{\frac{7.5T_{d}}{273.3+T_{d}}}

                Where T_{d}=Dew Point, E= Actual Vapor Pressure

  • Now calculate the Relative Humidity(RH) by dividing Actual Vapor Pressure by Saturated Vapor Pressure and multiplying by 100.

RH=\frac{E}{E_{s}}X100    Eq(3)

The sling psychrometer can also be used to measure dew point. Dew point is simply the relative humidity with 100 per cent or complete saturated state, condensation starts at that point. Dew Point around 55 is preferable for human beings.

Crankshaft Position Sensor Diagram: Detailed Insights

Crankshaft Position Sensor as the name indicates it is a type of sensing device. In this article we will discuss about Crankshaft Position Sensor Diagram.

Crankshaft Position Sensor Diagram has importance in both petrol and diesel engines because Crankshaft Position Sensor is an electronic device most widely used to detect ignition timing and engine RPM. This diagram helps in proper installation of the sensor.

To maintain the efficiency of a car’s engine it is necessary to maintain a suggested speed by all the internal parts. To make it possible the crankshaft position sensor must senses the precise position of the crankshaft. In automobile engineering Crankshaft Position Sensor is commonly abbreviated as CKP.

What is a Crankshaft Position Sensor?

The main function of a crankshaft position sensor is to investigate the position or rotational speed of the crankshaft in both petrol and diesel engines.

Crankshaft Position Sensors perform multiple activities, mainly it monitors the exact movement of the crankshaft and in turn we get other related important parameters like engine speed and ignition and fuel injection timing. Engine speed in RPM can also measured by using these sensors.

crankshaft position sensor diagram
Crankshaft Position Sensor; Image credit: Wikipedia

Depending on model, year of manufacturing and making the crankshaft position sensor wiring diagram are quite different from each other. Generally the manufacturer of these sensors decide the wiring diagram as per the requirement and demand in the market.

For different brands of Position Sensors the color of wires are different and color codes also vary as per the brands. Before wiring a specific make and model of sensor one has to check the car’s owner manual.

Crankshaft Position Sensor Working

CKP is placed very near to the reluctor ring so that the teeth attached to it rotates close to the sensor tip. There is a gap maintained in between the reluctor teeth to give the ECU a reference point to the crankshaft rotation or position.

With the rotation of the crankshaft, a pulsed voltage signal is produced by the sensor, each pulse is corresponding to the teeth of the reluctor ring.

Using these signals the engine control unit to determine the exact timing of fuel injection or spark ignition and in which cylinder. If anyone of the cylinders misfires, the signal from the cylinder also indicates it. Whenever the signal from the sensor is missing the control unit stops spark and fuel injector won’t operate.

Engine fan with Hall effect sensor; Image Credit: Wikipedia

2 Wire Crank Sensor Wiring Diagram

The two-wire crankshaft position sensor consists of a Signal Wire, a Ground Wire and an ECU.

In 2 wire crank sensor, the function of the signal wire to send the voltage from position sensor to the ECU(Electronic Control Unit). The ground wire is required to complete the electric circuit. Both of these wires are connected to ECU.

2 Wire Crank Sensor

2 wire crank sensor is an inductive type sensor which consists of sensor magnet and winding coil and a toothed wheel. As the reluctor ring or the toothed wheel comes closer to the crank sensor, the magnetic field fluctuates as a result voltage is produced in the wiring coil. This voltage or signal is sent to the ECU which will calculate the position of the crankshaft.

Inductive type position sensors does not require any external voltage source wire to energize it. When any item comes near to it produces the voltage itself. The Crankshaft Position Sensor Diagram for 2Wire is given below:

2 Wire Crankshaft Position Sensor Diagram

Crankshaft Position Sensor diagrams are different depending on the type and model of the sensors.

3 Wire Crank Sensor Wiring Diagram

3 wire crank sensor mainly consists of 3 wires, reference voltage, signal and ground wire. This type of sensors are classified as hall effect type sensor.

A 3 wire crank sensor has a magnet and a steel type material like germanium and a transistor. As soon as the toothed wheel comes near the sensor, the magnetic flux of the magnet in the sensor changes and as a result voltage is produced. This voltage is ampliphied by the transistor and sent to the car computer.

3 Wire Crank Sensor

Additional external voltage is required in 3 wire crank sensor. This type of sensor has an integrated circuit and an outside power source is necessary to work which amplifies the voltage.

That’s why it has three wires, earth, voltage, and a signal wire. The Crankshaft Position Sensor Diagram for 3 Wire is given below:

3 Wire Crankshaft Position Sensor Diagram

Crankshaft Motion

A crankshaft plays an important role inside an IC Engine by transforming the reciprocating movement of the piston into rotary motion.

In a reciprocating engine, using a connecting rod piston and crankshaft are connected so that reciprocating motion of the piston can be delivered to the crankshaft. After receiving this reciprocating motion from piston via connecting rod, crankshaft changes it into rotary motion.

Crankshaft is essential to get rotary motion for the flywheel which ultimately responsible for moving the car wheels.

9+ Relative Humidity Example: Detailed Facts

Relative humidity is the measurement of water vapor present in the air. In this article, we will discuss different Examples.

Relative humidity(RH or ɸ) indicates the amount of water vapor in the air in comparison to the amount of water vapor the air can possibly hold at that particular temperature. A relative humidity of 50% means the air holds only half of water vapor it can actually hold.

Relative Humidity Examples are listed below:

It is responsible for safety and durability of machineries, cars, houses etc. and it affects greatly the health, comfort and security of human being.

Weather Forecasting

Measurement of relative humidity helps in weather forecasting. Prediction for rain, fog or moist occurring in atmosphere can be done with the help of humidity monitoring.

Accurate and reliable prediction is of great importance in all fields concerning global climate changes like the hydrological phase and ablation of glaciers.

A highly humid condition indicates more moisture content in the air, which means more possibilities for cloud formation, and if the temperature goes down rain falling also occurs. The weather is forecasted based on present weather patterns including wind and humidity and depending on long-term weather statistics.

Weather forecast; Image Credit: Wikipedia

Animal Husbandry

The animal raising conditions in livestock stations and poultry houses play vital roles in both animal health and production. Relative Humidity has adverse effects on animal welfare including poor growth and development.

The high humid condition may cause stress on the animal respiratory system and many infectious diseases. Correct monitoring and controlling could result in significant improvement in animal husbandry.

relative humidity example
Animal husbandry; Image Credit: Flickr

Moisture around products

Controlling humidity around the final output is important as extreme humid conditions affect the product, therefore continuous monitoring is essential in food production industries. If we consider the chocolate industry, the relative humidity in storage should be maintained at a predetermined level.

If the humid level rises above the required level and remains at that level for a long time, moisture starts forming on the surface of the chocolate leading to dissolving of sugar.

After the evaporation of moisture, sugar starts forming crystals which gives a white, dusty, grainy appearance on the chocolate surface. This phenomenon is known as sugar blooming .

Characteristics of pharmaceutical products

Pharmaceutical products are generally highly sensitive to moisture content so improper humid condition becomes a great threat for pharmaceutical companies also.

Controlling accurate humid levels is essential and medicines in the form of pills, and dry powders should be kept in a controlled condition. Moisture content more than the required level alters the properties of the medicines to such an extent that medicines become useless.

Air Conditioners

Relative humidity plays a crucial role in maintaining the efficiency of HVAC systems used in residential houses and commercial buildings.

 A highly humid condition inside a home, force the air conditioner to work overtime to maintain a comfortable atmosphere. It leads to less efficiency of the air conditioner and require frequent maintenance, at the same time we may face a hike in energy bills.

Air conditioning condenser units outside a building; Image Credit: Wikipedia

Another negative impact of it is that it cancels out the cooling effect of the AC, even though the continuous running of air conditioning system we cannot derive the expected result. In simple words in spite paying more to cool your home wont cool it that effectively.

In low humid conditions, an occupant might experience aggravate allergies, eye irritations, stuffy nose, and chances of more spread of viral infections.

Building Materials

Relative Humidity has harsh impact on building materials also which may lead to high amount of monetary loss. A highly humid situation decreases the compressive strength of concrete affecting its durability. Moisture content enhances microbial growth like mold, bacteria, dust mites, fungi mildew, etc.

In case of concrete flooring, if the concrete is not sufficiently dry before floor laying it may cause the floor to swell, blister and crack. In that case only option left behind is complete replacement of the floor which is quite expensive and time consuming.

Excessive humid weather causes dampness inside the home and creates a unpleasant musty odor .

Agriculture and crop quality

Relative humidity is the most difficult factor to control in a greenhouse for the perfect growth of crops and plants. Highly humid condition results problems like foliar and root diseases, loss of quality, loss in yields etc. Requirement of more pesticides for disease control gives the plant a weak and stretched growth.

The too low situation results in a slow rate of plant growth and crops need a much longer period to get the saleable size; dropping off lower leaves, and low quality are also associated with low humidity.

Both the low and high humid conditions, the lower grade of quality reduce the selling price of crops and increases production costs and hinders greatly the overall profit.

Greenhouse; Image Credit: Wikipedia

Cooling Tower

To know the exact efficiency of the cooling tower, monitoring of relative humidity of atmosphere is necessary.

Relative humidity in air does affect the rate of evaporation from the tower. In refineries, regular monitoring is done to know the cooling efficiency of the tower.

 If temperature increases it will lead to a decrease in relative humidity, thus the air will become drier whereas when temperature decreases, the air will become wet means it will increase.

Cold Storage

Maintaining an accurate humid condition inside cold storage is vital because food products are hygroscopic in nature and their properties and texture vary with the humidity of air in the circumstances, not only with the temperature change. Accurate humid condition is necessary from economic point of view.

Fruits, vegetables, meat, dairy products(like paneer, cheeses), and other foodstuffs are stored at low temperature to enable their logistics within the cold chain and a correct humid control in cold storage is necessary.

Right humid atmosphere ensures that the product quality is maintained, the fresh look of the vegetables and fruits increases the price, profitability is high due to maintained product weight, longer storage and greater self-life reduces waste.

Cold Storage; Image Credit: Flickr

Voltage vs Voltage Drop: Comparative Analysis

This article illustrates the key differences between voltage vs voltage drop. We often refer to voltage and voltage drop as the same entities. But the fact is that they are different and possess unique attributes.

Here are the basic differences between voltage vs voltage drop-

ParametersVoltageVoltage drop
DefinitionVoltage is the electrical pressure that drives charged electrons to flow from one place to another through a conducting material. We can also say, voltage is the difference of electric potential between two points in a circuit.Voltage drop is also a quantity associated with voltage, but it is not exactly the same as voltage. Voltage drop is the potential difference caused in presence of any obstacle in the circuit such as resistor, inductor or capacitor. It is the lost voltage.
Meaning in DCIn one directional DC current flow, as per ohm’s law, voltage is the simple product of current and resistance. DC voltage is constant.DC voltage drop is the potential difference from one point to another point when DC current passes through any resistive component between the points. 
Meaning in ACAC current flows bi directionally or changes its polarity over a certain period of time. Due to this change, voltage also varied periodically. It is the product of current and impedance.The concept of AC voltage drop is similar to DC voltage drop. Just like AC voltage, AC voltage drop considers impedance in a circuit instead of only resistance.
CalculationVoltage is calculated using ohm’s law, by multiplying current and resistance. In capacitive and inductive circuits, capacitance and inductance are also taken into account along with resistance.Voltage drop calculation is just the same as voltage calculation as it is a part of voltage itself. Just in a circuit, voltage drop refers to only the drops occurred through reactances, but not the supply or source voltage.
MeasurementVoltage is measured with analog or digital voltmeter or multimeter. As voltage drop is a fraction of net voltage, it is measured with the same instrument used to measure the voltage.
Multimeter for measuring voltage vs voltage drop
Multimeter for measuring voltage and voltage drop; Image Credits: Wikipedia

When voltage and voltage drop can be the same?

Voltage and voltage drop is slightly different from each other. When we talk about the voltage vs voltage drop across any component such as resistor, capacitor or inductor in a circuit, it is the same as the voltage across it. 

Suppose, there are two resistors in a series configuration. A source voltage is fed to the circuit. The voltage is the supply voltage as well as the voltages through the individual resistors. But individual voltages will be the only voltage drops in the circuit. This applies for DC as well as AC circuits like RC, LR or RLC circuits.

Voltage vs voltage drop- FAQs

Electric potential vs voltage

Electric potential is known as the energy per unit charge attained or lost when any charge flows from a particular point with zero electric  potential. Voltage is the potential difference between any two points.

Let us take an example. Suppose, the potential of an arbitrary point P relative to a fixed point B is 100 volts, and the potential of the point Q is said to be 120 volts. Then the voltage or potential difference between the points P and Q is (120-100) = 20 volt. Here 100 volt and 120 volt are the electric potentials but 20 volt is the voltage. 

Voltage vs voltage drop in a circuit

What are the reasons of voltage vs voltage drop in a circuit?

Voltage is a very basic property of charge. It is the driving force that moves the electrons from one point to another and changes magnitude. Voltage is generated through electro chemical reaction or magnetic induction.

Voltage drop is typically caused by the effect of resistors, capacitors and inductors in the circuit. When current flows through a closed circuit where these reactive elements are there, supply voltage decreases when current meets any element. The more the reactance, the more the voltage vs voltage drop.

Voltage Divider In Series: What, Why, Working, Applications, Detailed Facts

In this article, we shall learn about voltage divider in series. Voltage divider is known to be a linear electrical circuit that provides the output voltage in terms of the input voltage. It is the connection of resistors in series.

A voltage divider is always a series circuit. The simplest voltage divider consists of two resistances in series. Voltage division is essential in creating a variable voltage that helps in voltage measurement, creating complex circuitry. The output voltage obtained by voltage division is a fraction of the input voltage.

What is voltage divider circuit?

A voltage divider is a simple linear circuit with passive elements. It works on the principle of voltage drop in resistors in series connection. While voltage differs in case of a voltage divider, current remains the same.

A potentiometer is one of the most commonly used  devices that utilizes voltage divider. We can apply a voltage across the terminals of the potentiometer and generate the output voltage. This voltage is proportional to the  position of the sliding contact. By moving this contact, we can change the voltage.

Poly-800: Potentiometers
Potentiometer: An application of voltage divider; Image Credit: Flickr

Voltage divider in series rule?

Voltage divider in series rule gives us an idea about the output voltage in the circuit obtained in terms of input voltage and resistance present in the circuit. Voltage divider in series rule follows ohm’s law.

Voltage drop is the result of current passing through a resistor. This voltage drop is directly proportional to the magnitude of the resistor. According to the rule, voltage across any resistor of the voltage divider is the product of net voltage and a fraction. This fraction is the ratio of that resistance and the equivalent resistance.

Why use voltage divider in series?

Only a series circuit is capable of voltage division as voltage drops in individual resistors while current passes. In a parallel circuit, the voltage remains the same and current is the quantity that gets divided.

As the name suggests, a voltage divider in series divides the total voltage into two parts which are equal or non equal. If we had to consider the parallel circuit, voltage would have been the same for each branch. In series, there is no branching. The current flows from one resistor to another and drops some value.

Voltage divider in series- FAQs

Voltage divider formula for resistors in series

Voltage divider rule says that, the voltage gets divided between two resistive components that are connected in series and these divided voltages are functions of input voltage and the series resistances.

voltage divider in series circuit
Resistive Voltage divider in series; Image Credits: Pinterest

Here, from ohm’s law, we get,

Voltage through R1,  V_{1}= iR_{1}

Voltage through R2,  V_{2}= iR_{2}

Applying kirchoff’s law, we can write,

 -V_{in} + V_{1} + V_{2}= 0

 V_{in} = V_{1} + V_{2}= iR_{1} + iR_{2} = i\left ( R_{1}+ R_{2} \right )

Therefore,  i = \frac{ V_{in}} {R_{1}+ R_{2}}

Again applying KVL, we can write,

 V_{out} - iR_{2} = 0

Or,  V_{out}= iR_{2} = \frac{ V_{in}} {R_{1}+ R_{2}}\times R_{2}

This is the required divided output voltage.

Voltage divider rule for capacitors in series

Voltage divider in series rule is just the same as the resistors. Here, the capacitive reactance is analogous to the resistance. The ability of the capacitors to oppose the current flow is known as capacitive reactance.

Capacitive voltage divider in series
Capacitive voltage divider in series; Image credits: Seekpng

Capacitive reactance,  X_{C} = \frac{1} {2\pi fC} where f is the frequency and C is the capacitance.

Therefore, if the net capacitive reactance is XC’ in series then  X_{C'} = \frac{1} {2\pi fC_{eq}}

Equivalent capacitance in series  C_{eq} = \frac{C_{1}C_{2}} {C_{1}+C_{2}}

 X_{C'} = \frac{1} {2\pi f \times \frac{C_{1}C_{2}} {C_{1}+C_{2}}}

So, current  i= \frac{V_{in}} {X_{C'}}

Now,  V_{out}= iX_{C_{2}}= \frac{V_{in}} {X_{C'}}\times \frac{1} {2\pi fC_{2}}

How to calculate voltage in voltage divider?

Voltage dividers are very essential components in amplifiers and controlling circuits. We can calculate voltages in a voltage divider circuit using some simple formulas derived by ohm’s law and kirchhoff’s law. 

For calculating the voltage through any resistor, we have to multiply the current with the ratio of that resistance value and equivalent series resistance of the voltage divider. If there’s other elements such as capacitors, the procedure will be the same. Only the resistance will be reactance in that case. 

Click to Read more on Voltage vs Voltage Drop: Comparative Analysis.

Center Tap Transformer: What, Why, Working, Applications, Detailed Facts

This article describes the center tap transformer, its components, working and other important details. A center tap is a wiring drawn from the midway of a transformer, a resistor, an inductor or a potentiometer.

A Center Tap transformer functions almost in the same way as an ordinary transformer. The only difference is that the tap present in the secondary winding of the center tap transformer divides the transformer into two parts, therefore, we can get two individual voltages across the two line ends if the transformer.

What is center tap transformer?

A center tap transformer is a device that has tapping through the middle of its secondary winding. This way, we can get half of the voltage induced in the secondary winding from the center tap to either of the tap ends.

A center tapped transformer is also known as the ” two phase three wire” transformer. These transformers work best in rectifier circuits and step down actions as it provides two output cycles for a single input cycle. For example, a V volt transformer measures V/2 Volts each across its two half windings made by center tapping it. 

Why do you center tap a transformer?

Center tap transformers play a pivotal role in uninterrupted and even voltage. Tapping helps in voltage regulation by changing the coil turn ratio. It can increase or decrease the voltage to compensate for the rise/loss. 

Center tapped transformer is essential as it converts the total AC input into DC output. Center tap in the secondary winding of the transformer generates a closed circuit in both first and second half cycle of the AC input. Therefore, center tap on the secondary is important in getting the positive half cycle on the load. 

Center tap transformer working

The working principle of the center tapped transformer is the same as any other transformer. When AC current flows through the primary coil of the center tap transformer, it creates a magnetic flux in the core of it.

When the secondary winding comes near to the primary, a magnetic flux induces in the secondary winding. This happens because the flux flows through the iron core and changes the direction with each AC cycle. Thus the AC current also passes through the two halves formed in the secondary winding and flows to the entire circuit.

Center tap transformer applications

Full wave rectifiers are the most significant application of center tap transformers. A full wave rectifier needs the entire DC output from the AC signal. The center tap transformer does this by allowing current in both cycles.

Other DC rectifier circuits use center tap transformers for converting full AC waves to DC. A normal transformer generates the output in only one direction while tapping through the mid of the transformer provides both direction output. Also, center tapping is seen in general step down transformers for AC-AC conversion.

Center tap transformer diagram

center tap transformer
Center tapped transformer diagram

In a center tap transformer, along with the usual coils, an extra wire is connected from the midpoint of the secondary. This point acts as a neutral point and divides the secondary voltage into two equal halves.

A center-tap transformer is designed in such a way that it can produce two secondary voltages with the same connection. Two voltages VS1 and VS2 obtained by the center tap, are shown in figure 1. These voltages are proportional to the primary voltage VP and the values are the same. So, the power in each coil is equal.

Center tap transformer- FAQs

Center tap transformer winding

In a center tap transformer, the secondary winding is coiled in the same direction as the primary winding, such that both the secondary half winding voltages can add up. The equivalent structure is shown in figure 2.

Here, the end points of the primary winding are P1 and P2. The middle point of the secondary winding between the ends S1 and S2 is S’, the center tapped point . When we apply AC voltage between P1 and P2 , voltage gets induced between S1 and S2. Each half-winding voltage, sums up to the full winding voltage.

Center tapped transformer winding

Delta center tap transformer

Delta center tap transformer, or a high leg delta transformer, is a component in which the secondary winding is connected in delta configuration and it is center tapped. The equivalent circuit is shown in the image below..

Delta Center Tap Transformer
High leg delta transformer; Image Credits: Wikipedia

We can see, one coil in the delta circuit is center tapped. The voltages of the delta coils are the same. Therefore the voltage difference from one end of the center tapped winding and from any two of the other end points to the tapping point are respectively half and √3/2 of the voltage difference between two ends.

9+ Pressure Drag Example: Detailed facts

In this article we will discuss about different Pressure Drag Examples. The pressure drag depends on the cross sectional area of the body rather than the surface area exposed.

Pressure Drag Examples are frequently seen in our daily life. Pressure drag occurs due to the increased pressure on the front end and decreased pressure on the rear end of an object while travelling through a fluid.

Different examples of pressure drag are listed below:

  1. A spherical shaped body moving through air
  2. A bicycle
  3. Swimmers
  4. A cylindrical body
  5. A moving car
  6. An airfoil or aerofoil with large angle of attack
  7. A moving truck
  8. A skydiver falling through the sky
  9. A boat travelling in water
  10. A piece of brick

Pressure drag is also caused by stationary object around which fluid medium passes. Streamlining reduces the Pressure Drag.

A spherical shaped body moving through air

A spherical shaped body experience high pressure drag while moving through a fluid due to its shape. The more surface area the more air particles will hit and greater the resistance experienced by the body.

Due to the boundary layer separation in case of a spherical body low pressure wake is formed behind the body.

pressure drag example
Wind drag applied on a particular shape; Image Credit: Wikipedia

A bicycle

Aerodynamic drag is indeed a major resistive force in cycling, every bicyclist has to overcome the wind resistance. Pressure drag plays a major role in cycling, mainly caused by the air particles push together on the front facing surfaces and more spaced out on the back surfaces creating a vast pressure difference between front and back ends.

Every cyclist who has ever pedalled into a stiff headwind knows about wind resistance. It’s exhausting! In order to move forward, the cyclist must push through the mass of air in front of him.

Cyclist; Image credi: Wikipedia

Swimmers

Different forms of drag forces like friction, pressure and wave drag continuously act on a swimmer as he steps down in the pool to their final touch at the wall. Frictional drag occurs as a result of rubbing of water molecules with the body of the swimmer, a smoother body of the swimmer reduces friction to some extent.

While swimming at higher speed, there is an increase in pressure in the frontal region (head of the swimmer) creating a pressure difference between the two ends of the swimmer’s body. This difference in pressure generates turbulence behind the swimmer’s body, this extra resistance force is the pressure drag.

Wave drag occurs as a result of the swimmer’s body submerged in the water and partly out of the water. All the wave drag force is generated from the head and shoulder portion of swimmer’s body.

Swimmer; Image credi: Unsplash

A cylindrical body

A cylindrical body is an example of bluff body that means high pressure drag is created due to its shape. A bluff body is a body whose surface is not aligned with the streamlines whenever it is placed in a flow of air or liquid.

A cylinder offers less resistance in terms of frictional drag but a offers a large pressure drag due to the eddy formation after the body moves through a large wake region. 

A moving car

In case of a moving car, the magnitude of drag force is equal and acting in an opposite direction to the force that the engine creates at the wheels of the vehicle. Due to these two equal and opposite forces acting on the car, the net resulting force becomes zero and the car can maintain a constant speed.

If the we make the force produced by the engine zero by keeping the car in a neutral position for a while then only drag force acts on the car. At this condition, the net force is available on the car and the car decelerates.

Pressure drag comes from the eddying motions that are set up in the fluid by the passage of a body. The drag is associated with the formation of a wake in the flow.

A truck with flat frontal area experiences high air resistance than a sports car with streamlined body.

A moving car; Image Credit: Wikipedia

An aerofoil with large angle of attack

A flow which experiences an increased pressure is known as flow in adverse pressure gradient. After following this condition far enough boundary layer separates from the surface and creates eddies and vortices behind the body. As a result pressure drag increases(due to vast pressure differential between two ends) and lift decreases.

In case of an aerofoil with higher angle of attack, the adverse pressure gradient on the top rear portion produces a separated flow. Due to this separation, wake size increases and pressure loss occurs due to eddy formation. As a result pressure drag increases.

At a higher angle of attack, a large fraction of the flow above the top of the aerofoil may be separated, at this point pressure drag is higher than the viscous drag.

Airflow separating from a wing at a high angle of attack; Image Credit: Wikipedia

A moving truck

In case of a commercial truck the pressure drag or form drag is quite high due to the larger frontal cross sectional area. Pressure drag produced is greatly influenced by the shape and size of the object.

Bodies with a larger presented cross section experiences higher drag than thinner or streamlined objects.

Pressure drag follows the drag equation that it increases with the square of the speed and thus plays a great role for high speed vehicles.

The performance and fuel efficiency of a vehicle depends on two aerodynamic forces pressure drag and skin friction drag. An effort is always given to shape a body with less drag.

A Truck; Image Credit: Wikipedia

A skydiver falling through the sky

When a skydiver jumps from the airplane both air resistance or drag and gravitational force act on his body. Gravitational force remains constant but the air resistance increases with increase in earthbound velocity.

The force of the air particles striking the body can be changed by altering his body position (the cross sectional area of the body). This changes the velocity of the skydiver towards the earth.

The drag(resistance) force experienced by the body can be represented by the following formula:

R=0.5\times D\times p\times A\times v^{2}

Where D is the drag coefficient,

p is the density of the medium, in this case air,

 A is the cross-sectional area of the object, and

 v is velocity of the object.

Skydiver; Image Credit: Wikipedia

A boat travelling in water

When a boat passes through a fluid medium eddying motion set behind the body which results in pressure drag. This drag is associated with wake formation which can be observed behind a passing boat.

In comparison to friction drag, pressure drag is less sensitive to Reynolds number. Pressure drag is important for separated flows.

This drag force can be observed in the form of a wake seen behind a passing boat.

Wake formation behind a boat; Image Credit: Unsplash

A piece of brick

A piece of brick due to its bluff body like structure experiences high pressure drag when moves through a fluid.

For a bluff body dominant source of drag is pressure drag and always depend on the cross sectional area.

11+ Drag Force Example: Detailed facts

In this article, we will discuss different examples of drag Forces with detailed insights. Drag Forces are mechanical forces generated due to the interaction of a solid body with its surrounding fluid.

Drag Force Examples are very common and frequently seen in nature as the force acting opposite to the relative motion of any moving body. Whenever a body moves through air this resistive force is called aerodynamic drag and if the travelling medium is water, then it is known as hydrodynamic drag.

Drag Force Examples are listed below

A boat travelling in water

Forces on a boat result from motion of air which interact with the boat and results a motive power for sailing in water. The forces acting on the boat depend on wind speed and direction as well as the speed and direction of the craft.

Four forces act on the boat: its weight, the buoyant force (the contact force with the water that pushes the boat up), the forward force of the wind, and the backward drag of the water.

drag force example
A sailing boat; Image credit: Wikipedia

The drag force D experienced by a body while travelling through a fluid is given by,

D=\frac{1}{2}C\rho Av^{2}

Where:

C is the drag coefficient, typical values ranging from 0.4 to 1.0 for different fluids (such as air and water)

ρ is the density of the fluid through which the body is moving

v is the speed of the body relative to the fluid

A is the projected cross-sectional area of the body perpendicular to the flow direction .

An aeroplane flying in the sky

The combined outcome of four forces drag, thrust, lift and weight make it possible to fly an aeroplane in the sky.

 The weight of the aeroplane pulls it towards the centre of the earth, to overcome this pulling force enough lift in upward direction is required. Lift is the result of differences in air pressure on and above the aeroplane wings. Aeroplane engine produces thrust in the direction of motion of the plane which is balanced by the drag force acting opposite to the direction of motion.

When an airplane is flying straight and level at a constant speed, the lift it produces balances its weight, and the thrust it produces balances its drag. However, this balance of forces changes as the airplane rises and descends, as it speeds up and slows down, and as it turns.

Forces acting on an aeroplane in a steady level longitudinal flight ; Image Credit: Wikipedia

A bird flying in the sky

Flapping wings by bird is one of the widespread propulsion methods available in nature.

In case of a bird, the lift that is generated by flapping the wings can be considered as a vertical force that supports the weight of the bird’s body (i.e. downward gravitational pull). Here drag is considered as the horizontal force that opposes thrust. Thrust is the force that moves the object in the forward direction, for a bird the trust is provided by the muscles of the bird.

Drag is caused by air resistance and acts in the opposite direction of motion, drag produced depends on the shape of the object, density of air and the moving speed of that object. Thrust can either overcome or counteract the drag force.

During forward flight, a bird’s body generates drag that tends to decelerate its speed. By flapping its wings, or by converting potential energy into work if gliding, the bird produces both lift and thrust to balance the pull of gravity and drag

Forces acting on a wing; Image credit: Wikipedia

A moving car

In case of a moving car, the magnitude of drag force is equal and acting in an opposite direction to the force that the engine creates at the wheels of the vehicle. Due to these two equal and opposite forces acting on the car, the net resulting force becomes zero and the car can maintain a constant speed.

If the we make the force produced by the engine zero by keeping the car in a neutral position for a while then only drag force acts on the car. At this condition, the net force is available on the car and the car decelerates.

A Moving Car; Image Credit: Wikipedia

Riding a bicycle or bike

Bicyclist; image Credit: Wikipedia

Aerodynamic drag is indeed a major resistive force in cycling, every bicyclist has to overcome the wind resistance. Pressure drag plays a major role in cycling, mainly caused by the air particles push together on the front facing surfaces and more spaced out on the back surfaces

Every cyclist who has ever pedaled into a stiff headwind knows about wind resistance. It’s exhausting! In order to move forward, the cyclist must push through the mass of air in front of him.

Bike

Bicycles and motorcycles are both single-track vehicles and so their motions have many fundamental attributes in common. If we consider the biker and the bike as a single system the external forces acting are: drag force, gravitational force, inertia, frictional force from the ground and internal forces are caused by the rider.

Dynamics of a biker; Image Credit: Wikipedia

Parachute

The drag force acts on a parachute depends on the size of the parachute, larger the parachute higher will be the drag force acting on it.

The two forces acting on a parachute are drag force or air resistance and the gravitational force. Drag force acts in the opposite direction of gravitational force and slows down the parachute whenever it falls.

Parachute; Image Credit: Wikipedia

A skydiver falling through the sky

When a skydiver jumps from the airplane both air resistance or drag and gravitational force act on his body. Gravitational force remains constant but the air resistance increases with increase in earthbound velocity.

The force of the air particles striking the body can be changed by altering his body position (the cross sectional area of the body). This changes the velocity of the skydiver towards the earth.

The drag(resistance) force experienced by the body can be represented by the following formula:

R=0.5\times D\times p\times A\times v^{2}

Where D is the drag coefficient,

p is the density of the medium, in this case air,

 A is the cross-sectional area of the object, and

 v is velocity of the object.

Skidiving; Image Credit: Wikipedia

Motion of an arrows and frisbee

Trajectory of an arrow is influenced by three forces: a) force of acceleration from the bow towards the target, b) force of acceleration towards the earth due to gravitational force, and c) force of deceleration due to aerodynamic drag on the arrow.

The bow string force accelerates the arrow from the bow until the arrow reaches the launch velocity, drag force slows down its velocity as the arrow moves through the air. Finally the gravitational force brings back the arrow to the earth surface.

Large forces result in acceleration but heavy masses are very hard to accelerate or decelerate. Therefore, a lighter arrow leaves the bow at faster speed and loses velocity faster during the flight.

Runners  

When the runners run the “wind” they experience pushing against them is actually the force of drag. In case of a runner or swimmer the drag force is always acting against the motion, trying to slows down their motion. To overcome the drag a runner has to move fast to make the running forward. In other words more thrust should be produced by the body.

Swimmers

Different forms of drag forces like friction, pressure and wave drag continuously act on a swimmer as he steps down in the pool to their final touch at the wall. Frictional drag occurs as a result of rubbing of water molecules with the body of the swimmer, a smoother body of the swimmer reduces friction to some extent.

While swimming at higher speed, there is an increase in pressure in the frontal region (head of the swimmer) creating a pressure difference between the two ends of the swimmer’s body. This difference in pressure generates turbulence behind the swimmer’s body, this extra resistance force is the pressure drag.

Wave drag occurs as a result of the swimmer’s body submerged in the water and partly out of the water. All the wave drag force is generated from the head and shoulder portion of swimmer’s body.

Swimmer; Image Credit: Unsplash

Motion of balls

As the ball moves through air, Drag will resist the motion of the ball during its flight, and will reduce its range and height, at the same time crosswinds will deflect it from its original path. Both the effects are considered by the players in sports like golf.

A bouncing ball generally follows projectile motion, different forces act on a ball are drag force, gravitational force, magnus force due to ball’s spin and buoyant force, all the forces have to be considered to analyze ball’s motion.

In general, there are many factors that affect the magnitude of the drag force including the shape and size of the ball, the square of the velocity of the object, and conditions of the air; particularly, the density and viscosity of the air. Determining the magnitude of the drag force is difficult because it depends on the details of how the flow interacts with the surface of the object. For a soccer ball, this is particularly difficult because stitches are used to hold the ball together.

Bouncing Ball; Image Credit: Wikipedia

Isentropic Efficiency Of Nozzle: What, How, Several Types, Examples

The main purpose of using a nozzle is to accelerate the velocity of a flowing fluid using pressure. In this article we will discuss about Isentropic Efficiency of Nozzle.

Isentropic efficiency of nozzle is the ratio actual kinetic energy at nozzle exit and isentropic kinetic energy at nozzle exit for the same inlet and exit pressures.

A fluid accelerates in a nozzle as it is moving from high pressure to low pressure with an increase in kinetic energy. Frictional losses inside the nozzle decreases fluid KE and raise the temperature of the fluid, increasing its entropy.

isentropic efficiency of nozzle
A nozzle from the Ariane 5 rocket; Image Credit: wikipedia

A water nozzle; Image credit: wikipedia

Nozzles are operated under adiabatic condition but the ideal process for a nozzle is the isentropic process. To have a comparison between actual work done and work under isentropic conditions of a device, a parameter called Isentropic Efficiency is used.

What Is Isentropic Efficiency of Nozzle?

The isentropic process involves no irreversibilities and serves as the ideal process for adiabatic devices.

Turbines, compressors and nozzles works under adiabatic conditions. Since they are not truly isentropic, they are considered as isentropic for calculation point of view. Isentropic efficiency is the parameter for a nozzle, turbine or compressor which defines how efficiently these devices approximate a corresponding isentropic device.

Nearer to an idealized isentropic process, improved will be the performance of the nozzle.

IsentropicEfficiency of nozzle is generally greater than 95%. So losses due to irreversibilities are very small in case of a well designed nozzle.

What is a Nozzle?

Nozzles are most widely used steady flow device in steam turbines, gas turbines and rockets.

Nozzle is a device often a pipe or a tube of varying cross sectional area used to control the direction of flow as well as exit velocity, mass, shape and pressure of the flow. Inside a nozzle pressure energy is converted into kinetic energy or we can say the fluid velocity increases with an expense of pressure energy.

Depending on required velocity and mach number of the fluid, Nozzles can be categorised like Convergent type, Divergent type and Convergent-Divergent type. Nozzle can be used for both subsonic and supersonic flows.

A De Laval Nozzle; Image credit: Wikipedia

In the above figure, a de Laval nozzle, showing approximate flow velocity increasing from green to red in the direction of flow

Isentropic Efficiency of Nozzle Formula

Isentropic Efficiency represents the performance index of a nozzle. A comparison of nozzle’s performance relative to an isentropic process.

Isentropic Efficiency of Nozzle can be defined as the ratio of actual enthalpy drop to isentropic enthalpy drop between the same pressures.

Isentropic Efficiency of Nozzle=Actual enthalpy drop/Isentropic enthalpy drop

 \eta _{N}=\frac{h_{1}-h_{2a}}{h_{1}-h_{2s}}

Isentropic Efficiency formula is the measure of the deviation of actual processes from the corresponding idealized ones. The ratio of actual work done by a nozzle to work done by the nozzle under isentropic condition is called Isentropic Nozzle Efficiency.

Isentropic Efficiency of a nozzle(\eta _{N})= Actual Kinetic Energy at Nozzle Exit/ Isentropic Kinetic Energy at Nozzle Exit.

\eta _{N}=\frac{V_{2a}^{2}}{V_{2s}^{2}}

Theoretically the process inside the nozzle is considered as isentropic but due to frictional losses the process is irreversible.

Enthalpy Entropy diagram for a flow inside a nozzle

Process 1-2:Isentropic Process

Process1- 2{}’:Actual Process

Efficiency of nozzle, \eta _{nozzle}=\frac{h_{1}-{h_{2}}'}{h_{1}-h_{2}}   Eq(1)

For Process 1-2, applying SFEE, h_{1}+\frac{V_{1}^{2}}{2}=h_{2}+\frac{V_{2}^{2}}{2}

 Or, h_{1}-h_{2}=\frac{V_{2}^{2}-V_{1}^{2}}{2}    Eq(2)

For Process 1- 2{}', applying SFEE, h_{1}+\frac{V_{1}^{2}}{2}= {h_{2}}'+\frac{V_{2}^{2}}{2}

Or, h_{1}-{h_{2}}'=\frac{{V_{2}}'^{2}-V_{1}^{2}}{2}       Eq(3)

Now from Eq(1) substituting the values of h_{1}-h_{2}  and h_{1}-{h_{2}}' ,we get

\eta _{nozzle}=\frac{{V_{2}}'^{2}-V_{1}^{2}}{V_{2}^{2}-V_{1}^{2}}  Eq(4)

Equation(1) and (4) are the formulas to calculate the Isentropic Efficiency of Nozzle.

How to Find Isentropic Efficiency of Nozzle?

A Nozzle reduces the pressure of the flow and at the same time speed up the flow to create a thrust.

Some amount of heat loss takes place from the steam due to the friction with the surface of the nozzle. Frictional effect also increases the dryness fraction of steam, because energy lost in friction is transferred into heat which tends to dry or super heat the steam.

In case of fluid dynamics, stagnation point denotes a point where local velocity of a fluid remains zero and isentropic stagnation state represents a state when a flow of fluid goes through reversible adiabatic deceleration to zero velocity.

Both actual and isentropic states are used for gases.

Enthalpy Entropy Diagram for Stagnation State; Image credit: wikipedia

The actual stagnation state is obtained for actual deceleration to zero velocity, irreversibility may be also associated. For this reason stagnation property is sometimes reversed for actual state properties, and the term total property is applied for isentropic stagnation states.

Both isentropic and actual stagnation states have same enthalpy, same temperature(for ideal gas) but may be pressure is more in case of isentropic stagnation state in comparison to actual stagnation state.

In case of a nozzle the inlet velocity is negligible in comparison to exit velocity of  a flow.

From the energy balance,h_{1}=h_{2a}+\frac{V_{2a}^{2}}{2}

Isentropic Efficiency of Nozzle=Actual enthalpy drop/Isentropic enthalpy drop

 \eta _{N}=\frac{h_{1}-h_{2a}}{h_{1}-h_{2s}}

Where h_{1}=specific enthalpy of the gas at the entrance

h_{2a}=specific enthalpy of gas at the exit for the actual process

h_{2s}= specific enthalpy of gas at the exit for the isentropic  process

Isentropic Efficiency Nozzle Example

Example: Steam enters a nozzle at 1.4 MPa  250^{\circ} C and negligible velocity and expands to 115 KPa and a quality of 97% dry. Determine the exit velocity of the steam.

Solution: Given data , Initial Pressure, P_{1}=1.4MPa

                                                                              = 1.4\times 10^{6} Pa

                                                                              =1.4\times 10\times 10^{5}

                                                                               =14 bar

Initial Temperature, T_{1}=250^{\circ} C

Final Pressure, P_{2}=115 KPa= 1.15\times 10^{5} Pa=1.15 bar

Quality of steam at exit, x_{2}=0.97

Exit Velocity, V_{2}=?

Neglecting initial velocity, Exit Velocity, V_{2}= 44.72\sqrt{h_{1}-h_{2}}= \sqrt{2000(h_{1}-h_{2})} m/s

Considering initial velocity, V_{2}=\sqrt{2000(h_{1}-h_{2})+V_{1}^{2}}

h_{1}=Enthalpy at initial condition i.e. at 1.14 MPa i.e at 14 bar 250^{\circ} C, from steam tables,

h_{1}=2927.6 KJ/Kg

h_{2}=Enthalpy at exit condition i.e. at 115 KPa i.e at 1.15 bar x_{2}=0.97, from steam tables

h_{f2}=434.2 KJ/kg

h_{fg2}=2247.4 KJ/kg

h_{2}=h_{f2}+x_{2}h_{fg2}=434.2+0.97X2247.4=2614.18 KJ/Kg

Hence the exit velocity of steam,

V_{2}=44.72\sqrt{2927.6-2614.18}=791.7m/s

11+ Thermal Equilibrium Example: Detailed Explanations

In this article “Thermal equilibrium example” will be discuss with detailed explanations. Thermal equilibrium example is very important concept to understand the changing of state for a substance.

11+ Thermal Equilibrium Example is encounter in below,

Refrigerator:-

Refrigerator is a device which is appropriate example of thermal expansion. When a food item is stored in the refrigerator that time the item will start to goes down its temperature and the temperature of the refrigerator and the temperature of food item will be same and the process of temperature changing for the food item will be stop.

Refrigerator is a home appliance and commercial appliance. The refrigerator carry a compartment with thermal insulator and also a heat pump through which heat easily can transfer from its midst to its external surrounding. For this process the inside temperature of the refrigerator will be lower than the temperature of the room.

Thermal equilibrium example
Image – Refrigerator;
Image Credit – Wikimedia Commons

Oven:-

Oven is a device which is also an appropriate example of thermal expansion. When a food item is placed in an oven and heat is applied on it that time the item will start to goes up its temperature. When the temperature of the oven and the temperature of food item will be same that time the process of temperature changing between the oven and the food item will be stop.

An oven is use for cooking purpose and also heats the food item to a wished temperature.

Image – Grilled chicken in a oven;
Image Credit – Wikimedia Commons

Types of oven:

Types of oven is listed below,

  1. Electric oven
  2. Gas oven
  3. Earth oven
  4. Masonry oven
  5. Toaster oven
  6. Ceramic oven
  7. Wall oven
  8. Steam oven
  9. Microwave oven

Melting of a ice cube:-

Another example of thermal expansion is melting of an ice cube. When an ice cube placed on a normal temperature its try to reaching at the room temperature and melting point will be increases at this particular time ice cube start to changing its state from solid to liquid.

Image – Melting of a ice cube;
Image Credit – Wikimedia Commons

Freezing of water:-

Another example of thermal expansion is freezing of water. When water is placed on a lower temperature its try to reaching at the lower temperature from the normal temperature at this particular time water starts to change its state from liquid to solid.

Drying of wet hair:-

Drying of wet hair is another regular example of thermal expansion. When we dry our wet hair in normal room temperature that time our wet hair reach at the room temperature and hair will be dry.

Drying of wet clothes:-

Drying of wet clothes is another regular example of thermal expansion. When we dry our wet clothes in normal room temperature that time our wet clothes reach at the room temperature and cloth will be dry.

Cooling of a cup of tea:-

Cooling of a cup of tea is another regular example of thermal expansion. When a cup of tea is placed on a normal room temperature that time a cup of tea try to reaching at the room temperature and boiling point will be decreases. A cup of tea starts to change its temperature and became cool.

Image – Cooling of a cup of tea;
Image Credit – Wikimedia Commons

Melting of ice-cream:-

Another example of thermal expansion is melting of ice cream. When ice cream is placed on a normal room temperature that time its try to reaching at the room temperature and melting point will be increases and freezing point will be decreases. The ice cream starts to change its state from solid to liquid.

Image – Melting of ice cream;
Image Credit – Wikimedia Commons

Freezing of ice- cream:-

Another example of thermal expansion is freezing of ice cream. When ice cream is placed on a refrigerator that time ice cream try to reaching at the refrigerant temperature and melting point will be decreases and freezing point will be increases. For this particular reason the ice cream starts to change its state from liquid to solid.

Cooling of a hot rod:-

Cooling of a hot rod is another example of thermal expansion. When a rod has higher temperature after doing any operation it became hotter. When a hotter rod is placed in a normal room temperature that time the rod try to reach at the room temperature. The rod starts to decreases its temperature and became cool.

Making of tea:-

When we make tea that time with hot water milk is added at that time the temperature of milk is low and the temperature of water is cold but when hot water and cold milk is added to each the mixture comes in a normal temperature. So, making of tea is also another example of thermal expansion.

Frequent asked questions:-

Question: –

Write the formula for thermal equilibrium.

Solution: – When two different matters stay in same temperature that’s mean the two different matters maintain thermal equilibrium.

The formula for thermal equilibrium is,

Q = m * C_e * \Delta t

Where,

Q = Total energy of the specific matter of the body which is expressed in Joule

m = Mass of the specific matter of the body which is expressed in grams

C_e = Specific heat of the specific matter of the body which is expressed in joule per Kelvin per kilogram

\Delta t = (Final temperature – Starting temperature) of the specific matter of the body which is expressed in Kelvin

Question: –

In a house a bowl is present which is decorated with beautiful stones. The bowl is made with aluminium. The weight of the bowl is 15 gram and temperature is about 39 degree centigrade. Now in the aluminium bowl water is placed. At this condition the temperature of the water will be 20 degree centigrade and weight of the water is about 32 gram.

Find the exact temperature where the temperature of the aluminium and the temperature of the water will be same.

Solution: –

We know that,

Q = m * C_e * \Delta t

Where,

Q = Total energy of the specific matter of the body

m = Mass of the specific matter of the body

C_e = Specific heat of the specific matter of the body

\Delta t = (Final temperature – Starting temperature) of the specific matter of the body

For aluminium,

Q_A = m_A * C_e_A * \Delta t_A.............. eqn (1)

Given data are,

m_A =  15 gram

C_e_A  = 0.215 calorie per gram degree centigrade

\Delta t_A = (T_f - T_i_A) degree centigrade = (T_f - 39) degree centigrade

For water,

Q_W = m_W * C_e_W * \Delta t_W.............. eqn (1)

Given data are,

m_W = 32 gram

C_e_W = 1 calorie per gram degree centigrade

\Delta t_W = (T_f - T_i_W) degree centigrade = (T_f - 20) degree centigrade

Now, from………….. eqn (1) and ………….. eqn (2) we can write,

Q_A = m_A * C_e_A * \Delta t_A = (-) Q_W = (-) m_W * C_e_W * \Delta t_W

Putting the value from eqn (1) and eqn (2),

15 \times (0.215) \times (T_f - 39) = (-) 32 \times 1 \times (T_f - 20)

(Put the value for C_e_W = 1 calorie per gram degree centigrade)

3.225 \times (T_f - 39) = -32 (T_f - 20)

3.225 T_f - 125.775 = -32 T_f + 640

3.225 T_f + 32 T_f = 640 + 125.775

T_f = \frac{640 + 125.775}{35.225}

T_f = 21.7 degree centigrade

In a house a bowl is present which is decorated with beautiful stones. The bowl is made with aluminium. The weight of the bowl is 15 gram and temperature is about 39 degree centigrade. Now in the aluminium bowl water is placed. At this condition the temperature of the water will be 20 degree centigrade and weight of the water is about 32 gram

The exact temperature where the temperature of the aluminium and the temperature of the water will be same is 21.7 degree centigrade

Question: –

Explain types of thermodynamic equilibrium.

Solution: – A system is called thermodynamic equilibrium when mechanical equilibrium, thermal equilibrium and chemical equilibrium are same.

Thermodynamic equilibrium three types, they are,

Mechanical equilibrium:-

A system is called mechanical equilibrium when pressure will be no changed in any condition and also no changes in acting of unbalanced force.

Thermal equilibrium:-

A system is called thermal equilibrium when temperature will be no changed in any condition inside the system of the matter.

Chemical equilibrium:-

A system is called chemical equilibrium when chemical reaction no present inside the system and also any type of composition changes is not present of the matter.