Keerthana Srikumar

Gravitational potential energy to elastic potential energy is one of the rarest of combination of energy conversion. So describing it would need a detailed review of the topic in detailed format.

When we say that gravitational potential energy to elastic potential energy, both have different explanation. We shall discuss few examples to understand the concept of the energy conversion from gravitational potential energy to elastic potential energy.

• Bungee Jumping
• Elastic Band Pulled Downward

Bungee Jumping

Bungee Jumping is one of the good examples for the conversion process of gravitational potential energy to elastic energy.

The person is tied in hip with proper safety care and let lose in air, this is a good show cast of the gravitational potential energy coming into action.

Here mainly tensional force comes into play so when the weight is let down the tension force acts and the to and fro movement is observed.

So instantly the rope with the weight is pulled backwards. It shows that the gravitational potential energy to elastic potential energy conversion happens immediately and is one of the good examples.

Elastic Band Pulled Downward

When any elastic band or rubber band is pulled downward there is an observation of gravitational potential energy to elastic potential energy conversion taking place.

When the band is at rest is possess potential energy and when it is pulled downward it will possess gravitational potential energy. Also the band will be pulled back to its original position instantly which proves the theory of elastic potential energy.

The original position is called as the elastic potential energy. So the pulling movement of band is regarded to be the elastic potential energy.

How are gravitational potential and elastic potential energy related?

Generally the gravitational potential energy is the weight of the object in the presence of gravity. And the elastic potential energy is regarded to be the potential energy of the object mainly of the shape.

There is a formula which will tell us the relationship between the gravitational potential energy to elastic potential energy, and that is (GPE=weight x height).

How is gravitational potential energy converted to elastic potential energy?

In the universe not every object is acted upon its own, it requires certain energy related to its work. So here when we talk about the gravitational potential energy we generally talk about the object which possesses potential energy including gravity.

The conversion of gravitational potential energy to elastic potential energy is very much subtle and observed as a linear conversion of energy.  For instance, in a spring the energy is stored as compressed energy and when released it will convert as elastic potential energy.

When gravitational potential energy is converted to elastic potential energy?

Let us take an example of a spring, this show that gravitational potential energy to elastic potential energy conversion is possible. So when the spring is being pulled downward the gravitational potential energy comes into play.

Later when the spring goes back to its original position we see the action of elastic potential energy into play. So by this way, the to and fro movement is when the gravitational potential energy to elastic potential energy conversion talks place.

Where is gravitational potential energy converted to elastic potential energy?

The gravitational potential energy to elastic potential energy conversion takes place in between the to and fro movement of the elastic object that is under action of force. The conversion of potential energy into different form talks place here.

When we let the elastic bank lose, that is when we pull the band it will automatically come back to its original position, and this exactly where the gravitational potential energy to elastic potential energy conversion takes place.

Gravitational potential energy to elastic potential energy formula

The general formula for the gravitational potential energy to elastic potential energy is given as,

GPE= weight x height.

Here we need to know the terms well, the GPE means it is gravitational potential energy, weight and height is regarded to the functions of the object under force.

Generally the gravitational potential energy is the potential energy of the object which is regarded to be under motion. The elastic potential energy is the normal potential energy of the object and this mainly depends on the shape of the object.

Gravitational potential energy to elastic potential energy efficiency

Generally when we need to find the efficiency of the potential energy there is a formula,    Eg= mgh. And we can use the same formula in order to find the efficiency of the gravitational potential energy to elastic potential energy.

Basically mgh means, mass, gravity and height of the particular object that is been subjected to the potential energy. So here we know that although gravity and elasticity is been included the potential energy remain the same.

Conclusion

Gravitational potential energy to elastic potential energy conversion takes place here and we have seen all the possibilities of how, where and when the energy conversion takes place. Along with this we also have seen the formula and the efficiency of the potential energy in terms of conversion.

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Gravitational potential energy to electrical energy conversion is one of the energy that occur in nature all by its own and spontaneous. This kind energy transfer is quite rare to witness and very few examples could be cited.

Gravitational potential energy means when the potential energy is been witnessed due to the gravitational force been applied. Potential energy is put into work due gravitational force presence. We shall see few examples regarding gravitational potential energy to electrical energy.

• Hydroelectric Dam
• Gravity Battery
• Falling Electric Toy Car
• Gravitationally Powered Dynamo

Hydroelectric Dam

Generally a dam is constructed over heavy flowing river or stream in order to collect the excess water in a particular area. The man built dam has several types in itself and hydroelectric is one of those.

One of the types is the hydroelectric dam which will collect the water behind the dam and will store the water until release. The gravitational potential energy helps the water to flow and hit the shafts in the turbine.

Here in this type of dam the water will be stored at the back end, when required the water will be released and this will help the turbine to wind around. Instantly, the electricity is generated when the turbines rotates in a constant motion.

So it is how the gravitational potential energy is converted to the electrical energy in such hydroelectric dams.

Gravity Battery

Gravity battery is one of the types of battery which stores the energy in it as gravitational potential energy. The device has a grid in it which stores the excess energy and it will used as electrical energy.

Basically a battery is a device which stores energy which can be put into use when in need. The energy in it is first stores as potential energy, also when it comes to gravity battery the energy is simply stored as gravity potential energy.

So when we use the battery for several purposes the energy stored as gravity potential energy is now converted to chemical energy which in turn finally used as electrical energy. by this way we can tell that the conversion of gravitational potential energy to electrical energy takes place.

Falling Electric Toy Car

The electronic toy car which falls can also be considered under the category of energy conversion of gravitational potential energy to electrical energy. Basically this is just an imaginative section where we can find the concepts deep in this section.

Let’s assume an electric car which works horizontally, that is a conventional car which runs straight and this converts the potential energy to electrical energy. But what happens if the electric car is made to run vertically and falls under gravity is the question here.

When an electric car is run over a surface and made to run in the downward direction the gravitational potential energy comes into play so here the gravitational potential energy to electrical energy conversion takes places.

Gravitationally Powered Dynamo

Generally a dynamo is device inside a generator which creates energy when the commutator rotates. But gravitationally powered dynamo is the one which stores energy in terms of gravity and that we call it as the gravity potential energy.

Dynamo is one single device which is let to operate within the generator in order to produce electricity. In context to gravity the dynamo will store the energy in terms of gravitational potential energy which is put into use for later.

How are gravitational potential and electrical energy related?

Battery is one of the famous examples which work on the conversion of potential energy to electrical energy. But here in this section we are dealing with the gravitational potential energy.

Similarly the gravitational potential energy is the one which stores gravitational energy in terms of potential energy and it is converted to the electrical energy. It is the process where the electrical energy is been converted from the potential energy.

By this way we will understand the whole process of conversion of such energy is rare to witness and very few examples exists to explain such phenomenon.

How is gravitational potential energy converted to electrical energy?

Let us see this using an example, in a hydroelectric dam the water is stored at the back of the dam. The stored water possesses some energy in terms of potential energy and when the water is let out it basically flows downwards.

So when the water falls downwards while stored it will fall on the turbine and make it to move. This in turn will rotate the shafts which produces the electricity. It is how the energy conversion of gravitational potential energy to electrical energy takes place in general per se.

Conversion of potential energy to electrical energy could be executed using certain devices. So for example the grids in a device will store the gravitational energy as the potential energy which could be converted to any energy.

When gravitational potential energy is converted to electrical energy?

The gravitational potential energy is converted to electrical energy when the potential energy to converted to electrical energy having strong influence of gravity in the whole process.

Basically gravity means the pulling force which acts downward and the gravitational potential energy is simply the potential energy stored and released in downward direction.

Where is gravitational potential energy converted to electrical energy?

Hydro power plant is one of the good examples that explain where the energy conversion takes place. The hydro power plant is mainly built to produce electricity using the energy available in nature.

Basically the hydro power plant uses potential energy stored in water for further use. So when the water is released it will fall downwards due to gravity and this we call it as the gravitational potential energy.

So when the water falls the potential energy is converted to kinetic energy at that instant and then this energy finally used to generate electricity which is the conversion of gravitational potential energy to electrical energy.

Gravitational potential energy to electrical energy formula

Although there is no exact formula for gravitational potential energy to electrical energy but we can rearrange the formula of the potential energy to kinetic energy and modify according to the needs.

The formula for potential energy to electrical energy is given by,

V = k × [q/r]

Where, v= potential energy; k=kinetic energy; q= charge responsible for the movement of electron; r= distance between any point to the centre of the charge.

Gravitational potential energy to electrical energy efficiency

Efficiency of a particular energy conversion, that is, the gravitational potential energy to electrical energy depends on the kind of device which converts it in presence of strong gravity influence.

For example when hydroelectric dam has enough efficiency in order to convert the potential energy to electrical energy under strong influence of gravity we know that the conversion has well taken place.

The hydroelectric dams have 95% of efficiency and some have 80%, these depends on the speed of water and how much energy is been converted.

Summary

We now know that gravitational potential energy cannot be directly converted to electrical energy directly but there are other means too. So, it first has to be converted to kinetic energy and then to rest of the energy. And here we see that gravitational potential energy is primarily converted to kinetic energy and later to electrical energy.

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Tidal energy examples are far more explainable than the tidal energy itself. In recent times the tidal energy has found itself a place to be into research.

The tidal energy examples will show us how the energy creation works and the kind of consumption goes into the usage of such energy. Given below are few tidal energy examples.

• Turbines
• Electricity
• Tidal Power Plant
• Coastal Area

Turbines

Turbines are one of the most used examples for several energy sources. The turbines run with a shaft attached to it. Like the wind turbines there are tidal turbines too. Tidal energy examples will fit into it.

When water is gushed out with a terrific force the energy produced by the turbines will make the shaft attached to it in movement. So when the shaft moves using the tidal energy and then the turbines work well within.

Tidal power plant has reversible turbines in it and there is also low hydrodynamic head which has mainly bidirectional flow in it. The bidirectional flow will help in the production of tidal energy as well as the water that flows due to it.

Electricity

Electricity is one of the major resources of energy conversion. Electricity is got form the tidal energy. The tidal energy will produce electricity which is supplied to the households.  Basically electricity is produced in terms of electric and magnetic fields.

When electric fields and magnetic fields are present then the electricity is easily created. But in conventional terms we make use of several other means in order to produce electricity. In terms of wind and tidal energy we get electricity in these ways too.

When high tides is been calculated it will hit the target and we get the tidal energy which in turn will be used to produce electricity.

Tidal Power Plant

There are several tidal power plants in and around the country. The tidal energy is one of the sufficient emery of all types. Once installed then the maintenance becomes easier so this is widely used in several countries.

Basically what happens in oceans is that, the tides are created by the gravitational energy from the sun, moon and so many celestial bodies. But mainly the gravitational energy of the moon is the reason for the ups and downs of the tides.

When the tides are calculated then the kinetic energy of the tides are been converted to so many other resources mainly electricity.

Tidal energy is considered to be the renewable energy of all energies. So the tidal energy examples are easier to be explained than any other energy sources.

Coastal Area

Tidal energy is been very easy to apply to be applied in the coastal areas. The river banks are saved form the high and low tides of the ocean.

The tidal power plants are mainly situated in the coastal are mainly because the high and low tides are more conventional to calculate by the engineers. Water is denser than air so the energy created by the tides is more convenient to be used.

Tidal energy is chosen to be better than the wind mills as the low and high tides are been calculated easily and they are also available all the time, that is, they are the renewable energy system.

Tidal Energy Explanation

Tidal energy can be explained in so many ways but we make use of the tidal energy examples in order to understand the content better. Tidal energy is way more predictable than the wind or any other energy.

Tidal energy basically is when the tides hit each other with great force form which an energy is created so finally that energy is been used in several forms. When water moves at great speed they form tides and these tides when channel through particular area they create energy.

We also must know that installation of the tidal power plants is very much expensive since the capital investment is high. The equipment required to install the tidal power plant is quite a task.

Tidal Energy Uses

The tidal energy is predictable and the reason we say this is that, low tide and high tide can be measured by the engineer. When the tides are measured we can easily find out the amount of energy which is been crated and could also be put into use.

There are so many other uses of tidal energy and we shall see it in terms of tidal energy examples. So these tides will protect the coastal area from flooding. Due to the high tides formed around the coastal will protect it from the flooding.

Tidal energy is one of the non-exhaustible and renewable resources. They can get more and more each time. The tidal energy produces no pollution and they do not affect the greenhouse. The energy density of tides is way more efficient than any other energy sources.

Other energy sources require high maintenance despite the installation charges. But in tidal energy even though the installation is expensive the maintenance is low.

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Electrical energy can be converted to sound energy through various methods, such as the use of piezoelectric materials, electromagnetic transducers, and diaphragms. The conversion process involves the generation of sound waves from electrical energy, which can then be harnessed for different applications, including energy harvesting, audio systems, and various industrial and medical applications.

Understanding the Conversion Process

The conversion of electrical energy to sound energy can be explained by the principles of piezoelectricity and electromagnetism.

Piezoelectricity

Piezoelectricity is a phenomenon where certain materials, such as quartz crystals, can generate an electrical charge when subjected to mechanical stress or strain. This property can be used to convert sound wave energy into electrical energy.

When a piezoelectric material is compressed, its crystal structure changes, and it acquires a net charge. This charge can be converted into an electrical current, which can then be used to power various devices or be stored for later use.

The amount of electrical energy generated by a piezoelectric material depends on several factors, including the material’s piezoelectric coefficient, the applied mechanical stress, and the size of the material.

Piezoelectric Coefficient Formula:
$d = \frac{Q}{F}$

Where:
– $d$ is the piezoelectric coefficient (in C/N or m/V)
– $Q$ is the electric charge generated (in Coulombs)
– $F$ is the applied force (in Newtons)

Example:
Consider a piezoelectric crystal with a piezoelectric coefficient of 2.1 × 10^-10 C/N. If a force of 10 N is applied to the crystal, the generated electric charge would be:
$Q = d \times F = 2.1 \times 10^{-10} \times 10 = 2.1 \times 10^{-9} C$

Electromagnetism

Electromagnetic transducers, such as those used in audio speakers, can also be used to convert sound waves into electrical energy. This process involves the use of a coil and a magnet.

When sound waves hit the diaphragm of an audio speaker, the coil moves back and forth within the magnetic field, generating an electrical current. The amount of electrical energy generated depends on the strength of the magnetic field, the number of turns in the coil, and the velocity of the coil’s movement.

Electromagnetic Induction Formula:
$\varepsilon = -N \frac{d\Phi}{dt}$

Where:
– $\varepsilon$ is the induced electromotive force (in Volts)
– $N$ is the number of turns in the coil
– $\Phi$ is the magnetic flux (in Webers)
– $t$ is the time (in seconds)

Example:
Consider an audio speaker with a coil of 100 turns, placed in a magnetic field with a flux density of 0.5 T. If the coil moves at a velocity of 1 m/s, the induced electromotive force would be:
$\varepsilon = -N \frac{d\Phi}{dt} = -100 \times 0.5 \times 1 = -50 V$

Quantifying the Conversion Process

The conversion of noise to electric energy using piezoelectric materials can be quantified by calculating the equivalent noise level (L) for specific locations.

Equivalent Noise Level (L)

The equivalent noise level (L) is a measure of the average sound level over a given period of time, typically expressed in decibels (dB). It is calculated using the following formula:

$L = 10 \log \left( \frac{1}{T} \int_{0}^{T} 10^{\frac{p(t)}{10}} dt \right)$

Where:
– $L$ is the equivalent noise level (in dB)
– $T$ is the time period (in seconds)
– $p(t)$ is the instantaneous sound pressure level (in dB)

Example:
In a study conducted in three bus stations in Alexandria, the equivalent noise level values were found to exceed the permissible limits during the daytime, evening, and night:
– Daytime: 75-85 dB (10-20 dB higher than the permissible limit)
– Evening: 80-85 dB (20-25 dB higher than the permissible limit)
– Night: 75-80 dB (20-25 dB higher than the permissible limit)

Electric Energy Production

The electric energy produced from an area of 1.45 m^2 containing 690 piezoelectric QB220-503YB transducers at each of the selected bus stations was about 0.024 watt-hours. This amount of electric energy is too small to be used in a practical application.

To produce beneficial electric energy, the application area should be maximized to hundreds of square meters. This would allow for the generation of enough electric energy to power a single LED street lamp or be stored for use in applications that require greater amounts of electrical energy.

Theoretical Considerations

The conversion of electrical energy to sound energy can be further understood by considering the theoretical principles involved.

Piezoelectric Effect

The piezoelectric effect is the ability of certain materials, such as quartz crystals, to generate an electrical charge in response to applied mechanical stress or strain. This effect is reversible, meaning that the application of an electrical field can also cause the material to deform.

The piezoelectric effect is described by the following equation:

$P = d \times T$

Where:
– $P$ is the polarization (in C/m^2)
– $d$ is the piezoelectric coefficient (in C/N or m/V)
– $T$ is the applied stress (in N/m^2)

Electromagnetic Induction

Electromagnetic induction is the process by which a changing magnetic field induces an electromotive force (EMF) in a conductor, such as a coil of wire. This effect is the basis for the operation of electromagnetic transducers, which can be used to convert sound waves into electrical energy.

The induced EMF is described by Faraday’s law of electromagnetic induction:

$\varepsilon = -N \frac{d\Phi}{dt}$

Where:
– $\varepsilon$ is the induced EMF (in Volts)
– $N$ is the number of turns in the coil
– $\Phi$ is the magnetic flux (in Webers)
– $t$ is the time (in seconds)

Applications and Considerations

The conversion of electrical energy to sound energy has a wide range of applications, including:

1. Energy Harvesting: Piezoelectric and electromagnetic transducers can be used to harvest energy from ambient sound waves, such as those generated by machinery, traffic, or human activities. This energy can be used to power small electronic devices or be stored for later use.

2. Audio Systems: Electromagnetic transducers are the foundation of most audio speakers, converting electrical signals into sound waves. This technology is used in a wide range of audio equipment, from headphones and speakers to musical instruments and public address systems.

3. Industrial and Medical Applications: Piezoelectric materials are used in various industrial and medical applications, such as ultrasonic imaging, non-destructive testing, and vibration sensors.

When designing systems that convert electrical energy to sound energy, it is important to consider factors such as the efficiency of the conversion process, the power requirements of the application, and the environmental conditions (e.g., noise levels, temperature, humidity) that may affect the performance of the system.

Conclusion

The conversion of electrical energy to sound energy is a complex process that involves the principles of piezoelectricity and electromagnetism. By understanding the theoretical foundations and practical considerations of this process, engineers and researchers can develop innovative solutions for a wide range of applications, from energy harvesting to audio systems and beyond.

References

1. Svantek. (n.d.). Sound Energy. Retrieved from https://svantek.com/academy/sound-energy/
2. Just Energy. (2021, May 11). Sound Energy: Everything You Need to Know. Retrieved from https://justenergy.com/blog/sound-energy-everything-you-need-to-know/
3. U.S. Department of Energy. (n.d.). ISO 14001 Step 2.4: Identify Energy Sources and Uses. Retrieved from https://www1.eere.energy.gov/manufacturing/eguide/iso_step_2_4.html
4. Elsevier. (2019). Conversion of noise to electric energy using piezoelectric materials. Retrieved from https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6622490/
5. ResearchGate. (2021). Sound to electric energy generating device. Retrieved from https://www.researchgate.net/publication/352776217_Sound_to_electric_energy_generating_device

The conversion of chemical energy to kinetic energy is a fundamental process in thermodynamics that plays a crucial role in various physical and chemical phenomena. This process is governed by the laws of thermodynamics, specifically the first law, which states that energy cannot be created or destroyed but can be converted from one form to another.

The Kinetic Molecular Theory of Gases

The kinetic molecular theory of gases is a fundamental concept in chemistry and physics that explains the behavior of gases. According to this theory, gas particles are in constant motion and possess kinetic energy due to their motion. The kinetic energy of gas particles is directly proportional to the absolute temperature of the gas, as expressed by the equation:

$${\displaystyle \mathrm{E}=\frac{1}{2}m{u}^2}$$

where E is the kinetic energy, m is the mass of the particle, and u is the speed of the particle.

The distribution of molecular speeds in a gas is described by the Maxwell-Boltzmann distribution, which shows the number of molecules with a given speed at a particular temperature. The most probable speed (u_mp), average speed (u_av), and root-mean-square (rms) speed (u_rms) are important parameters that characterize the distribution of molecular speeds. These quantities are related to the temperature and mass of the gas molecules and can be calculated using the following equations:

$${\displaystyle u_{\mathrm{mp}}=\sqrt{\frac{2}{\pi }\mathrm{k}T}}\text{or}{\displaystyle u_{\mathrm{mp}}=\sqrt{\frac{2}{\pi }\frac{\mathrm{R}}{M}T}}\text{and}{\displaystyle u_{\mathrm{av}}=\sqrt{\frac{8}{\pi }\mathrm{k}T}}\text{or}{\displaystyle u_{\mathrm{av}}=\sqrt{\frac{8}{\pi }\frac{\mathrm{R}}{M}T}}\text{and}{\displaystyle u_{\mathrm{rms}}=\sqrt{\frac{3}{m}\mathrm{k}T}}\text{or}{\displaystyle u_{\mathrm{rms}}=\sqrt{\frac{3}{M}\frac{\mathrm{R}}{T}}}$$

where k is the Boltzmann constant, R is the gas constant, T is the temperature, and M is the molar mass of the gas.

Example: Calculating the rms Speed of CO₂ at 40°C

To calculate the root-mean-square (rms) speed of CO₂ at 40°C, we can use the following equation:

$${\displaystyle u_{\mathrm{rms}}=\sqrt{\frac{3}{M\frac{\mathrm{R}}{T}}}}$$

where:
– M = 44.01 g/mol (molar mass of CO₂)
– R = 8.314 J/(mol·K) (gas constant)
– T = 40 + 273.15 K (temperature in Kelvin)

Substituting the values, we get:

$${\displaystyle u_{\mathrm{rms}}=\sqrt{\frac{3}{44.01}\frac{8.314}{313.15}}}$$
$${\displaystyle \approx 421\text{m/s}}$$

Therefore, the rms speed of CO₂ at 40°C is approximately 421 m/s.

Thermochemistry

Thermochemistry is the study of the energy changes that occur during chemical reactions. The energy changes during a chemical reaction can be measured using various techniques, including calorimetry. Calorimetry is a technique that measures the heat absorbed or released during a chemical reaction or a physical change.

The energy change during a chemical reaction is often expressed in terms of the enthalpy change (ΔH) of the reaction. The enthalpy change is the difference between the enthalpy of the products and the enthalpy of the reactants. The enthalpy change can be calculated using the equation:

$${\displaystyle \mathrm{\Delta }H=\sum _i^n{H}_f°(products)-\sum _i^n{H}_f°(reactants)}$$

where ΔH is the enthalpy change, n is the stoichiometric coefficient of the species, and H_f^° is the standard enthalpy of formation of the species.

Example: Calculating the Enthalpy Change for the Combustion of Methane

To calculate the enthalpy change for the combustion of methane (CH₄), we can use the following equation:

$${\displaystyle \mathrm{\Delta }H=[-890.4kJ/\mathrm{mol}]-[-74.8kJ/\mathrm{mol}]=-815.6kJ/\mathrm{mol}}$$

Therefore, the enthalpy change for the combustion of methane is -815.6 kJ/mol.

Technical Specifications

The technical specifications for the conversion of chemical energy to kinetic energy and the measurement of enthalpy changes are as follows:

1. Kinetic Molecular Theory of Gases
2. Gas particles are in constant motion and possess kinetic energy due to their motion.
3. The kinetic energy of gas particles is directly proportional to the absolute temperature of the gas.
4. The distribution of molecular speeds in a gas is described by the Maxwell-Boltzmann distribution.

5. The most probable speed, average speed, and root-mean-square speed are important parameters that characterize the distribution of molecular speeds.

6. Enthalpy Change (ΔH)

7. The enthalpy change is the difference between the enthalpy of the products and the enthalpy of the reactants.
8. The enthalpy change can be calculated using the equation: ΔH = ∑nH_f^°(products) – ∑nH_f^°(reactants).
9. The enthalpy change can be measured using calorimetry.

Example Problems

1. Kinetic Molecular Theory of Gases

Calculate the root-mean-square speed (u_rms) of nitrogen gas (N₂) at 25°C.

Solution:

$${\displaystyle u_{\mathrm{rms}}=\sqrt{\frac{3}{M\frac{\mathrm{R}}{T}}}}$$

where M = 28.01 g/mol (molar mass of N₂), R = 8.314 J/(mol·K) (gas constant), and T = 25 + 273.15 K (temperature in Kelvin).

Substituting the values, we get:

$${\displaystyle u_{\mathrm{rms}}=\sqrt{\frac{3}{28.01}\frac{8.314}{298.15}}}$$

$${\displaystyle \approx 515\text{m/s}}$$

Therefore, the root-mean-square speed of nitrogen gas at 25°C is approximately 515 m/s.

1. Enthalpy Change (ΔH)

Calculate the enthalpy change (ΔH) for the combustion of propane (C₃H₈):

C₃H₈(g) + 5O₂(g) → 3CO₂(g) + 4H₂O(l)

Given:
– H_f^°(C₃H₈(g)) = -103.8 kJ/mol
– H_f^°(CO₂(g)) = -393.5 kJ/mol
– H_f^°(H₂O(l)) = -285.8 kJ/mol

Solution:

$${\displaystyle \mathrm{\Delta }H=[-3\times 393.5kJ/\mathrm{mol}+4\times 285.8kJ/\mathrm{mol}]-[-103.8kJ/\mathrm{mol}]}$$