Isothermal Process - Definition, Example, Formula, FAQs
  • Isothermal Process - Definition, Example, Formula, FAQs

Isothermal Process - Definition, Example, Formula, FAQs

Vishal kumarUpdated on 02 Jul 2025, 04:30 PM IST

In this article, we will discuss the Isothermal Process which is a thermodynamic process in which the temperature of a system remains constant throughout the process. In real life, we can observe isothermal processes in refrigeration and air conditioning systems, where gases are compressed and expanded while maintaining a constant temperature to regulate cooling. Let's discuss the concept of the Isothermal process in detail

This Story also Contains

  1. What is an Isothermal Process?
  2. Isothermal Process Formula
  3. Work Done in the Isothermal Process
  4. PV Diagram for the Isothermal Process
  5. Isothermal Process Examples
  6. Solved Examples of Isothermal Process
Isothermal Process - Definition, Example, Formula, FAQs
isothermal process

What is an Isothermal Process?

An isothermal process is a type of thermodynamic process where the temperature of the system remains constant throughout the entire process. In this process, the system exchanges heat with its surroundings to maintain this constant temperature, despite changes in other properties like pressure or volume

What is Isotherm?

If we observe the relation between temperature and any other thermodynamic variable such as pressure, volume, and others and draw a graph on the Cartesian plane then, all the curves which represent two states of a system where the temperature is the same during an isothermal process are called isotherms.

So, Those curves or lines which represent two states of a system at the same temperature in an isothermal process are called an isotherm.

For example, a line drawn as shown in the diagram below has two states A and B and both are at the same temperature during an isothermal process so this line is called an isotherm. We can consider any other thermodynamic variable on the X-axis.

Isothermal Process

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Isothermal Process Formula

The basic formula in thermodynamics which shows that two states are in the isothermal process is simply written as

$P_1 V_1=P_2 V_2$

where,

  • P represents the pressure and
  • V represents the volume of an isothermal process in two states 1 and 2

Work Done in the Isothermal Process

When a system undergoes an isothermal process, either work is done on it or work is done by it and this work is different for different processes.

In the isothermal process work done by the system is calculated using the formula:

$W=2.303 R T \log _{10}\left(V_2 N_1\right)$

where,

  • V represents volume at two different states being at a constant temperature of T and R is the universal gas constant.

PV Diagram for the Isothermal Process

A diagram representation of the pressure and volume of an isothermal process on a cartesian plane is called a PV diagram for an isothermal process and it is best shown in the diagram given below:

PV Diagram for isothermal process

Change in Internal Energy in the Isothermal Process

The internal energy of any thermodynamic system is calculated as

∆U=nCv∆T

where,

  • n represents the total number of moles of a gas
  • C represents the specific heat of the gas but at constant volume
  • T represents temperature

Related Terms

In an isothermal process, the change in temperature is zero because of the constant temperature in the isothermal process. So, In an isothermal process, the change in internal energy is zero.

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Isothermal Process Examples

  1. When ice melts at a temperature of zero degrees then the whole ice melts but the temperature of the system remains the same over the period of time, hence this is an example of an isothermal process.
  2. All the thermodynamic reactions which occur inside the refrigerator are isothermal processes because the temperature of the refrigerator remains the same.
  3. and, all such thermodynamic processes which are carried out at constant magnitude of temperature will be considered as isothermal processes.

Solved Examples of Isothermal Process

1- Which of the following statements correctly describes the relationship between the slope of the isothermal curve and the slope of the adiabatic curve for a gas process?
1. Slope of the isothermal curve = Slope of the adiabatic curve
2. Slope of the isothermal curve $=\gamma \times$ Slope of the adiabatic curve
3. Slope of the adiabatic curve $=\gamma \times$ Slope of the isothermal curve
4. Slope of the adiabatic curve $=\frac{1}{2 \gamma} \times$ Slope of the isothermal curve

Solution:

Differentiating $P V=$ constant:

$$
\frac{d P}{d V}=-\frac{P}{V}
$$

Hence, the slope of the isothermal curve is:

$$
\text { Slope of isothermal curve }=-\frac{P}{V} \text {. }
$$

Differentiating $P V^\gamma=$ constant:

$$
\frac{d P}{d V}=-\gamma \frac{P}{V}
$$

Hence, the slope of the adiabatic curve is:

$$
\text { Slope of adiabatic curve }=-\gamma \frac{P}{V} .
$$

From the equations above:

$$
\left(\frac{d P}{d V}\right)_{\text {adiabatic }}=\gamma\left(\frac{d P}{d V}\right)_{\text {isothermal }} .
$$

Hence, the answer is the option 3.

2- 2 moles of an ideal is isothermally expanded to 3 times its original volume at 300 K . Calculate the Work done and heat absorbed by the gas?
Given ( $\mathrm{R}=8.31 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ and $\log _e 3=.4771$ )
Solution:

Here $\mathrm{n}=3, V_2=3 V_1, \mathrm{~T}=300 \mathrm{~K}$
Now using the above equation

$$
W=n R \operatorname{Tln}\left(\frac{V_2}{V_1}\right)
$$


Substituting the above values, we get

$$
W=5.48 \times 10^3 \mathrm{~J}
$$


Now heat absorbed $=$ Work done $=5.48 \times 10^3 \mathrm{~J}=1.31 \times 10^3 \mathrm{C}$

3. Draw the T-P diagram for the given P-V diagram for an ideal gas.

PV Diagram of ideal gas

Solution:
$$
P=\frac{\text { constant }}{V}
$$or$$
P V=\mathrm{constant}
$$

TP diagram of ideal gas
So it means temperature is constant. So here is the TP diagram

Frequently Asked Questions (FAQs)

Q: What is the significance of isothermal processes in the study of magnetic materials?
A:
Isothermal processes are important in studying the magnetic properties of materials. For example, isothermal magnetization curves show how the magnetization of a material changes with applied magnetic field at constant temperature, revealing important information about its magnetic behavior.
Q: How do isothermal processes relate to the concept of enthalpy?
A:
In an isothermal process, the change in enthalpy (H) is equal to the heat added to the system at constant pressure. This relationship is important in understanding heat transfer in various chemical and physical processes.
Q: What is the relationship between isothermal processes and the Joule-Thomson effect?
A:
The Joule-Thomson effect describes the temperature change of a gas when it expands through a valve. While the overall process is not isothermal, understanding isothermal processes helps in analyzing the thermodynamics of this effect.
Q: How do isothermal processes relate to the concept of thermodynamic potentials?
A:
Isothermal processes are crucial in defining and understanding thermodynamic potentials like Helmholtz free energy and Gibbs free energy. These potentials help predict the direction of spontaneous processes under constant temperature conditions.
Q: What is the significance of isothermal processes in the study of chemical equilibrium?
A:
Many chemical equilibrium processes occur under nearly isothermal conditions. Understanding isothermal processes is crucial for predicting how changes in pressure or concentration affect chemical equilibrium at constant temperature.
Q: How does the concept of isothermal processes apply to the behavior of superconductors?
A:
Superconductors exhibit perfect conductivity below a critical temperature. The transition between normal and superconducting states can be studied using isothermal processes, as temperature is a crucial parameter in superconductivity.
Q: What is the relationship between isothermal processes and the van der Waals equation?
A:
The van der Waals equation is a more realistic model of gas behavior than the ideal gas law. It can be used to analyze isothermal processes for real gases, accounting for molecular interactions and finite molecular size.
Q: What is the significance of isothermal processes in the study of osmosis?
A:
Osmosis, the movement of water across a semipermeable membrane, often occurs under nearly isothermal conditions. Understanding isothermal processes helps in analyzing the thermodynamics of osmotic pressure and related phenomena.
Q: How does the concept of isothermal processes apply to the behavior of elastomers?
A:
Elastomers, like rubber, exhibit interesting behavior under isothermal conditions. When stretched isothermally, they can actually absorb heat from the surroundings, contrary to most materials which release heat when stretched.
Q: What is the relationship between isothermal processes and the Clausius-Clapeyron equation?
A:
The Clausius-Clapeyron equation describes how the vapor pressure of a liquid changes with temperature. It's derived by considering two states in equilibrium at slightly different temperatures, effectively using isothermal processes.