**Content**

**Isothermal definition****Isothermal expansion****Isothermal compression****Isothermal vs. adiabatic****Isothermal calorimetry****Isothermal amplification****Isothermal nucleic acid amplification****Isothermal transformation diagram****Isothermal PV diagram****Isothermal process example****Isothermal work****Isothermal layer****Isothermal PCR****Isothermal process equation****Isothermal expansion of an ideal gas****Isothermal reversible expansion****Isothermal reaction****Isothermal irreversible expansion****Isothermal system****Isothermal bulk modulus****Isothermal internal energy****Isothermal compressibility coefficient****Isothermal heat transfer****Isothermal atmosphere****Isothermal surface****Isothermal conditions****Isothermal zone****Isothermal lines****Isothermal belt****Isothermal vs isobaric****Isothermal vs isentropic**

**Isothermal definition**

An isothermal process is a thermodynamic process. In this isothermal process, the system’s temperature remains constant throughout the process. If we consider temperature is T. The temperature change is ΔT.

For the isothermal process, we can say that ΔT = 0

**Isothermal expansion**

Isothermal expansion is increasing volume with a constant temperature of the system.

Isothermal – temperature constant

Expansion – Increasing volume

Let’s consider the piston-cylinder arrangement for understanding if the piston moves from BDC (Bottom dead center) to TDC (Top dead center) with a constant temperature of the gas. This isothermal process is considered as Isothermal expansion.

**Isothermal compression**

Isothermal compression is decreasing volume with a constant temperature of the system.

Isothermal – temperature constant

Compression – decreasing volume

Let’s consider another condition if the piston is moving from TDC to BDC (Bottom dead center) with a constant temperature of the gas. This isothermal process is considered Isothermal compression.

**Isothermal vs adiabatic**

Isothermal means Constant Temperature.

Adiabatic means Constant heat energy.

Some conditions for an isothermal process are :

- The temperature should remain constant.
- The variation must be happening at a slow rate.
- Specific heat of the gas is infinite.

Some basic conditions for adiabatic are as below :

- No heat transfer happens in adiabatic.
- The variation must happen at a very speedy.
- The specific heat of gas is 0 (Zero).

**Isothermal calorimetry**

It is one technique to find thermodynamic parameters’ interaction in a chemical solution. Using isothermal calorimetry, one can find binding affinity, binding stoichiometry, and enthalpy changes between two or more molecules interactions.

**Isothermal amplification**

It is one of the techniques used for pathogen monitoring. In this techniques, the DNA is amplified with keeping sensitivity higher than benchmark polymerase chain reaction (PCR)

**Isothermal nucleic acid amplification**

Isothermal amplification of nucleic acids is a technique that is efficient and faster accumulating nucleic acid at the isothermal process. It is a simple and efficient process. Since then, around 1990, many isothermal amplification processes have been developed as alternatives to a polymerase chain reaction (PCR)

**Isothermal transformation diagram**

An isothermal transformation diagram is used to understand the kinetics of steel. It is also known as the time-temperature- transformation diagram.

It is associated with mechanical properties, microconstituents/microstructures, and heat treatments in carbon steels.

**Isothermal PV diagram**

**Isothermal process example**

Isothermal is a process in which the system’s temperature remains unchanged or constant.

We can take the example of a refrigerator and heat pump. Here, in both cases, the heat energy is removed and added, but the system’s temperature remains constant.

Examples: Refrigerator, heat pump

**Isothermal work**

We have used the PV diagram above paragraph. If we want to write work done formula for it. We should consider the area under the curve A-B-VA-VB. The Work done for this integral can be given as,

[latex]W= nRT ln\frac{{Vb}}{Va}[/latex]

Here in the equation,

n is the number of moles

R is gas constant

T is the temperature in kelvin

**Isothermal layer**

An isothermal layer term is used in atmospheric science. It is defined as a vertical layer of air or gas with constant temperature throughout height. This situation is happening at the troposphere’s low level in various advection situations.

**Isothermal PCR**

The full form of PCR is a polymerase chain reaction. This reaction is used in isothermal amplification techniques to amplify DNA.

**Isothermal process equation**

If we consider universal gas law, then the equation is given as below,

PV = nRT

Now, here this is in isothermal process, so T = Constant,

PV = constant

The above equation holds good for a closed system containing ideal gas.

We have discussed the work done earlier. We can consider that equation for the isothermal process. As we know from figure Vb is the final volume, and Va is the initial volume.

[latex]W= nRT ln\frac{{Vb}}{Va}[/latex]

**Isothermal expansion of an ideal gas**

**Isothermal**– the temperature is constant.**Expansion**– the volume is increasing.

It means that isothermal expansion increases volume with a constant temperature of the system.

In this condition, the gas is doing **work**, so the work will be negative because the gas applies energy to increase in volume.

The change in internal energy is also zero ΔU = 0 (Ideal gas, Constant temperature)

[latex]Wrev = -\int_{Va}^{Va}P dV[/latex]

[latex]Wrev = -\int_{Va}^{Va}\frac{nRT}{V} dV[/latex]

[latex]Wrev = -nRTln\left | \frac{Vb}{Va} \right |[/latex]

**Isothermal reversible expansion**

This topic is covered in explaining the isothermal expansion of ideal gas.

**Isothermal reaction**

A chemical reaction occurring at one temperature, or we can say at a constant temperature, is an isothermal reaction. There no need for temperature change to continue reaction to end.

**Isothermal irreversible expansion**

An irreversible process is a real process we face in reality almost all the time. The system and its surrounding cannot be restored to their initial states.

**Isothermal system**

We have discussed the isothermal system in expansion and compression if we take piston-cylinder arrangement.

There are some assumptions for this system like,

- There is no friction between piston and cylinder
- There no heat or work loss from the system
- The internal energy of the system should be constant throughout the isothermal process.

If we supply heat at the bottom of the cylinder, then the piston will move from BDC to TDC, as shown in Figure. It is an isothermal expansion. Similarly, in isothermal compression reverse, as we have explained earlier. This complete system is isothermal.

**Isothermal bulk modulus**

Bulk modulus is reciprocal of compressibility.

[latex]B(isothermal) = -\frac{\Delta P}{\frac{\Delta V}{V}}[/latex]

Here, the term is the isothermal bulk modulus. It can be defined as the ratio of change in pressure to change in volume at a constant temperature. It is equal to P (pressure) if we solve the above equation.

**Isothermal internal energy**

We have discussed earlier that the constant temperature process’s internal energy remains constant.

**Isothermal compressibility coefficient**

The isothermal compressibility coefficient can be taken as the change of volume per unit change in pressure. It is also known as oil compressibility. It is widely used in resource estimation of oil or gas in petroleum study.

[latex]C(isothermal) = -\frac{1}{V}\cdot \frac{\Delta P}{\Delta V}[/latex]

**Isothermal heat transfer**

The expansion and compression process at constant temperature work on the principle of zero degradation energy. If the temperature is constant, then internal energy change and enthalpy change are zero. So, heat transfer is the same as work transfer.

If we heat the gas in any cylinder, then the gas’s temperature will increase. We want a system at a constant temperature, so we have to put one sink (cold source) to reject gained temperature.

Suppose we consider a cylinder with a piston. The gas will expand in the cylinder, and the piston gives displacement work due to getting heated. The temperature will stay constant in this case also.

**Isothermal atmosphere**

It can be defined as the there is no change in temperature with height in the atmosphere, and the pressure is decreasing exponentially with moving upward. It is also known as exponential atmosphere. We can say that the atmosphere is in hydrostatic equilibrium.

In this type of atmosphere, we can calculate the thickness between two adjacent heights with the equation given below,

[latex]Z2-Z1 =\frac{RT}{g} ln\frac{P1}{P2}[/latex]

Where,

Z1 & Z2 are two different heights,

P1 & P2 are Pressures at Z1 & Z2, respectively,

R is gas constant for dry air,

T is the virtual temperature in K,

g is gravitational acceleration in m/s^{2}

**Isothermal surface**

Suppose we consider any surface flat, circular, or curvature, etc. If all the points on that surface are at the same temperature, then we can say that the surface is isothermal.

**Isothermal conditions**

As my word, we know that the system’s temperature must stay constant in this isothermal process. To keep the temperature constant, the system is free to change other parameters like pressure, volume, etc. It is also possible during this process, the work-energy and heat energy can be changed, but the temperature remains the same.

**Isothermal zone**

This word is generally used in atmospheric science. It is a zone in the atmosphere where the relative temperature is constant at some kilometer height. Generally, it is in the lower part of the stratosphere. This zone provides convenient aircraft conditions because of its constant temperature, general access to clouds and rains, etc.

**Isothermal lines**

This word is used in geography. Suppose we draw a line on a map of the earth for connecting different places whose temperature is the same or near to the same. It is known as an isothermal line in general.

Here, each point reflects the particular temperature for reading taken in a period of time.

**Isothermal belt**

In 1858 Silas McDowell of Franklin, given this name for western North Carolina, Rutherford, and Polk countries. This term is used for a season in these zones when one can grow fruits, vegetables, etc., easily due to temperature consistency.

**Isothermal vs isobaric**

Isothermal – temperature constant

Isobaric – Pressure constant

Let’s compare both processes for work done. According to the figure, you can notice both processes. As we know, that work done is an area under the integral. In the figure, we can easily see that the isobaric process area is more so obviously, work done more in isobaric. There is some condition for it. The initial pressure and volume should be the same. This is not true because we never get work during isobaric in any of the thermodynamic cycles. This topic is logical.

The correct answer depends on the type of condition that volume is increased or decreased in the process.

**Isothermal vs isentropic**

Isothermal – temperature constant

Isentropic – Entropy constant

Let’s consider the compression process to understand it,

In isothermal compression, the piston is compressing gas very slowly. As much slowly to maintain the constant temperature of the system.

Whereas in the case of isentropic, there should be no heat transfer possible between the system and surrounding. The isentropic compression will occur without heat transfer with constant entropy.

The isentropic process is similar to adiabatic, where there is no heat transfer. The system for the isentropic process should be well insulated for heat loss. The isentropic compression process always gives more work output due to no heat loss.

**FAQs**

**Is there heat transfer in the Isothermal process?**

Answer: Yes, now the question is why and how?

Let’s consider a piston-cylinder example to understand it,

If heat is supplied to the bottom of the cylinder. The temperature will be maintained constant, and the piston will move. Either expansion or compression process. The heat is transferred, but the system’s temperature will stay the same as it is. This is why during the Carnot cycle, heat is added at a constant temperature.

**Why Isothermal process is very slow?**

It is necessary that the Isothermal process occurs slowly. Now see, the heat transfer is possible by keeping the system’s temperature constant. It means there is a thermal equilibrium of the system with the body. The process’s timing is slow to keep this thermal equilibrium and constant temperature. The time required for effective heat transfer will be higher, making the process slow.

**Isothermal process example problems**

There are many applications in day-to-day life with a constant temperature. Some of them are explained as below,

- The temperature inside the refrigerator is maintained
- It is possible to melt the ice by keeping the temperature constant at 0°C
- The phase change process occurs at a constant temperature, evaporation, and condensation
- Heat pump which works opposite to refrigeration

**What are some real-life examples of an Isothermal process**?

There is a huge number of example can be possible for this question. Kindly refer above questions.

Any phase change process occurring at constant temperature is an example of an isothermal process.

Evaporation of water from sea and river,

Freezing of water and melting of ice.

**Why does Isothermal process be more efficient than the adiabatic process?**

Let’s consider the reversible process. If the process is expansion, then the isothermal process’s work is more than adiabatic. You can notice by a diagram. The work done is an area under the curve.

Suppose the process is compression, then opposite to the above sentence. The work done in the adiabatic process is more.

To judge this question depends on every condition. As per the above condition, the isothermal process is more efficient than the adiabatic.

**What will be the specific heat for an Isothermal process an adiabatic process, and why**?

The specific heat can be defined as the amount of heat is required to raise the temperature of a substance by 1 degree.

[latex]Q = m Cp \Delta T[/latex]

If the process is the constant temperature, the ΔT = 0, so the specific heat is undefined or infinite.

Cp = Infinite (if temperature is constant)

For adiabatic process, the heat transfer is not possible , Q = 0

Cp = 0 (heat transfer is 0)

**In an Isothermal process, the change in internal energy is 0 Why**?

Internal energy is the function of the kinetic energy of the molecules.

The temperature indicates the average kinetic energy of molecules associated with the system.

If the temperature remains constant, then there is no change in kinetic energy. Hence, the internal energy remains constant. The change in internal energy is zero.

**What is more efficient Isothermal compression or isentropic compression, And why**?

The isentropic process occurs at constant entropy with no heat transfer. This process is always ideal and reversible. In the isentropic compression process, the system’s internal energy is increasing as there is no possibility of heat transfer between the system and surrounding.

In isothermal compression, the process occurs very slowly as the temperature and internal energy stay constant. There is heat transfer between the system and the surrounding.

That’s why the isentropic compression process is more efficient.

**Does an Isothermal process have an enthalpy change?**

We can understand it clearly by the equation of enthalpy.

Enthalpy H is given as below,

Change in enthalpy = change in internal energy + change in PV

For constant temperature process,

Change in internal energy = 0,

Change in PV = 0.

That’s why to Change in enthalpy= 0

**Why is an adiabatic curve steeper than an Isothermal curve**?

In the adiabatic process, the system’s temperature is increasing during compression. It is decreasing during expansion. Due to this, this curve crosses the isothermal curve at a certain point in the diagram.

In isothermal, there is no change of temperature. The curve will not become steeper like adiabatic.

**What would happen if I increase the volume of a system in an Isothermal process with external energy?**

Suppose you increase the volume of the system. You want the system to be isothermal. You have to make another arrangement for maintaining temperature. The increasing of the volume decreases the pressure.

**What is so special about the word “reversible” in an Isothermal or an adiabatic process?**

The first law of thermodynamics states that both of the processes sketched on the PV diagram are reversible mean. The system will come to its initial stage to stay in equilibrium.

**Why Isothermal and adiabatic in Carnot engine?**

The Carnot cycle is the most efficient in thermodynamics. The reason behind it is all the process in the cycle is reversible.

Carnot tried to transfer energy between two sources at constant temperature (Isothermal).

He tried to maximize the expansion work and minimize the required compression. He selected an adiabatic process for it.

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