Isothermal Process - Definition, Example, Formula, FAQs

Isothermal Process - Definition, Example, Formula, FAQs

Edited By Vishal kumar | Updated on Jul 02, 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 - Definition, Example, Formula, FAQs

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)

1. An adiabatic process occurs at constant (A) Temperature (B) Volume (C) Heat (D) None of the above.

Since, processes which occur at constant temperature are called isothermal processes. Process which occurs at constant magnitude of volume is called Isochoric. And, all the thermodynamic processes which occur at constant heat are called adiabatic processes, So, the correct option is (C) Heat.

2. Define Isothermal process.

The thermodynamics process in which the temperature of the whole system remains constant over a period of time is called isothermal process. So, the constant temperature of any system makes the process an isothermal process. For example, melting of ice at zero degree is such an example of an isothermal process.

3. Change in internal energy in isothermal process is (A) positive (B) negative (C) Depends upon the Volume of the gas. (D) zero.

In an isothermal process, the temperature of the system remains the same, so the change in temperature is always zero, and due to this the change in internal energy in an isothermal process is always zero, SO, the correct option is (D) zero.

4. During isothermal process, (A) Temperature remains the same. (B) Change in internal energy is zero. (C) Pressure is constant. (D) Volume changes slowly.

In an isothermal process, the temperature of the whole system is always the same and as well as the change in internal energy in isothermal process of the system is always zero. So, the correct option is During isothermal process (A) Temperature remains same and (B) Change in internal energy is zero.

5. For an ideal gas, in an isothermal process A. Heat content remains constant B. Heat content and temperature remain constant C. Temperature remains constant D. None of the above

Temperature remains constant.

6. In an isothermal expansion A. Internal energy of the gas increases B. Internal energy of the gas decreases C. Internal energy of the gas unchanged D. None of the above

Internal energy of the gas unchanged

7. Can two isothermal curves cut each other A. Never B. They will cut when temperature is 0 degree celsius C. Yes when pressure is critical pressure D. None of the above

Never

8. Can you give an example of an isothermal process in everyday life?
A common example of an approximate isothermal process is the expansion of air in a bicycle pump when it's compressed slowly. The heat generated is dissipated to the surroundings, keeping the temperature roughly constant.
9. What is the formula for work done in an isothermal process for an ideal gas?
The work done in an isothermal process for an ideal gas is given by W = nRT ln(V2/V1), where n is the number of moles, R is the gas constant, T is the constant temperature, and V2 and V1 are the final and initial volumes, respectively.
10. How does the speed of a process affect whether it can be considered isothermal?
For a process to be isothermal, it must occur slowly enough for heat to be exchanged with the surroundings, maintaining a constant temperature. Rapid processes are more likely to be adiabatic, as there's insufficient time for heat exchange.
11. How does the concept of isothermal processes relate to phase changes?
Phase changes, such as melting or boiling, are examples of isothermal processes. During these transitions, the temperature remains constant while heat is added or removed, changing the phase of the substance.
12. What is the significance of isothermal compression in the Carnot cycle?
Isothermal compression is one of the four stages in the Carnot cycle, an ideal thermodynamic cycle. It allows for efficient heat transfer between the system and the hot reservoir, contributing to the cycle's maximum theoretical efficiency.
13. What is an isothermal process?
An isothermal process is a thermodynamic process in which the temperature of the system remains constant throughout. During this process, heat is either added to or removed from the system to maintain a constant temperature while other properties like pressure and volume may change.
14. How does an isothermal process differ from an adiabatic process?
In an isothermal process, the temperature remains constant, and heat can be exchanged with the surroundings. In contrast, an adiabatic process involves no heat exchange with the surroundings, and the temperature of the system changes.
15. What is the key characteristic of the pressure-volume (P-V) diagram for an isothermal process?
The P-V diagram for an isothermal process is a hyperbola. This curve shows that as the volume increases, the pressure decreases, and vice versa, while maintaining a constant temperature.
16. Why is the internal energy of an ideal gas constant during an isothermal process?
For an ideal gas, the internal energy depends only on temperature. Since temperature remains constant in an isothermal process, the internal energy of an ideal gas also remains constant.
17. How does the First Law of Thermodynamics apply to an isothermal process?
In an isothermal process, the change in internal energy (ΔU) is zero. Therefore, according to the First Law (ΔU = Q - W), the heat added to the system (Q) must equal the work done by the system (W).
18. How does the entropy change in an isothermal process?
In an isothermal process, the entropy of the system changes. The change in entropy is given by ΔS = Q/T, where Q is the heat added to the system and T is the constant temperature.
19. What is the relationship between pressure and volume in an isothermal process for an ideal gas?
In an isothermal process for an ideal gas, pressure and volume are inversely proportional. This relationship is described by Boyle's Law: P1V1 = P2V2, where P and V represent pressure and volume at two different states.
20. How does an isothermal process differ from an isobaric process?
In an isothermal process, temperature remains constant while pressure and volume can change. In an isobaric process, pressure remains constant while temperature and volume can change.
21. Can a perfect isothermal process occur in reality?
A perfect isothermal process is an idealization. In reality, it's challenging to maintain a truly constant temperature throughout a process. However, many real-world processes can be approximated as isothermal if they occur slowly enough.
22. How does the ideal gas law apply to isothermal processes?
The ideal gas law (PV = nRT) applies to isothermal processes. Since temperature (T) is constant, the product of pressure (P) and volume (V) must also remain constant as the gas expands or contracts.
23. What is the role of a thermal reservoir in an isothermal process?
A thermal reservoir is a theoretical body with infinite heat capacity that can add or remove heat from a system without changing its own temperature. It's crucial for maintaining the constant temperature in an isothermal process.
24. How does the efficiency of an isothermal process compare to that of an adiabatic process?
Isothermal processes are generally more efficient than adiabatic processes because they allow for heat exchange with the surroundings. This heat exchange can be used to do work, whereas in adiabatic processes, no heat is exchanged.
25. What happens to the average kinetic energy of gas molecules during an isothermal process?
The average kinetic energy of gas molecules remains constant during an isothermal process. This is because temperature, which is directly proportional to the average kinetic energy of molecules, stays constant.
26. How does the concept of reversibility apply to isothermal processes?
An isothermal process can be reversible if it occurs infinitely slowly, allowing the system to always be in thermal equilibrium with its surroundings. In practice, most real isothermal processes are irreversible due to finite rates of heat transfer.
27. What is the significance of isothermal processes in thermodynamic cycles?
Isothermal processes are important in thermodynamic cycles because they allow for efficient heat transfer between the system and its surroundings. They are key components in ideal cycles like the Carnot cycle, which sets the upper limit for the efficiency of heat engines.
28. How does the work done in an isothermal expansion compare to that in an adiabatic expansion?
More work is done in an isothermal expansion than in an adiabatic expansion for the same initial and final volumes. This is because in an isothermal process, the system receives heat from the surroundings, which can be converted to additional work.
29. What is the relationship between heat and work in an isothermal process for an ideal gas?
For an ideal gas in an isothermal process, the heat added to the system equals the work done by the system. This is because the internal energy remains constant, so all heat input is converted to work output.
30. How does the concept of free expansion relate to isothermal processes?
Free expansion, where a gas expands into a vacuum, is not an isothermal process. It's an adiabatic process where no work is done and no heat is exchanged. An isothermal expansion, in contrast, involves heat transfer and work.
31. What is the significance of the isothermal bulk modulus in material science?
The isothermal bulk modulus describes a material's resistance to compression at constant temperature. It's important in understanding how materials behave under pressure in situations where temperature can be maintained constant.
32. How does the heat capacity of a system behave during an isothermal process?
The heat capacity of a system during an isothermal process is effectively infinite. This is because you can add or remove heat from the system without changing its temperature.
33. What is the difference between isothermal and quasi-static processes?
All isothermal processes are quasi-static (occurring slowly enough to maintain equilibrium), but not all quasi-static processes are isothermal. A quasi-static process can have changing temperature, while an isothermal process, by definition, has constant temperature.
34. How does the concept of isothermal processes apply to living organisms?
Many biological processes in warm-blooded animals occur under nearly isothermal conditions. The body maintains a constant internal temperature, allowing biochemical reactions to proceed efficiently regardless of external temperature fluctuations.
35. What is the relationship between isothermal processes and the Maxwell relations in thermodynamics?
The Maxwell relations, which connect different thermodynamic quantities, can be derived using isothermal processes. For example, one Maxwell relation shows how the change in entropy with volume at constant temperature relates to the change in pressure with temperature at constant volume.
36. How does an isothermal process affect the density of an ideal gas?
In an isothermal process, if the volume of an ideal gas increases, its density decreases, and vice versa. This is because density is mass per unit volume, and the mass remains constant while the volume changes.
37. What is the significance of isothermal processes in the study of phase diagrams?
Isothermal processes are represented by horizontal lines on phase diagrams. These lines show how a substance can change phase (e.g., from liquid to gas) at constant temperature by changing pressure.
38. How does the concept of isothermal compressibility relate to isothermal processes?
Isothermal compressibility measures how much the volume of a substance decreases under pressure at constant temperature. It's a key property in understanding how materials behave during isothermal compression.
39. What is the role of isothermal processes in the operation of refrigerators and heat pumps?
While real refrigeration cycles are not perfectly isothermal, they approximate isothermal processes in parts of their cycle. The evaporation and condensation stages in a refrigerator occur at nearly constant temperatures, similar to isothermal processes.
40. How does the speed of sound in a gas relate to isothermal processes?
The speed of sound in a gas depends on whether the process is isothermal or adiabatic. In very low frequency sound waves, the process is nearly isothermal, and the speed of sound is lower than in high-frequency waves, which are more adiabatic.
41. What is the significance of the isothermal atmosphere model in meteorology?
The isothermal atmosphere model assumes a constant temperature with altitude. While not entirely accurate, it provides a useful simplification for understanding certain atmospheric phenomena and serves as a baseline for more complex models.
42. How does the concept of isothermal processes apply to the expansion of the universe?
In cosmology, the very early universe is thought to have undergone periods of rapid expansion that were nearly isothermal. This concept is important in understanding the evolution and current state of the universe.
43. What is the relationship between isothermal processes and the Joule-Thomson effect?
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.
44. How do isothermal processes relate to the concept of thermodynamic potentials?
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.
45. What is the significance of isothermal processes in the study of chemical equilibrium?
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.
46. How does the concept of isothermal processes apply to the behavior of superconductors?
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.
47. What is the relationship between isothermal processes and the van der Waals equation?
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.
48. How do isothermal processes relate to the concept of enthalpy?
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.
49. What is the significance of isothermal processes in the study of osmosis?
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.
50. How does the concept of isothermal processes apply to the behavior of elastomers?
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.
51. What is the relationship between isothermal processes and the Clausius-Clapeyron equation?
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.
52. How do isothermal processes relate to the concept of fugacity in thermodynamics?
Fugacity is a measure of the tendency of a substance to escape from a phase. It's often used in place of pressure when dealing with non-ideal gases. Isothermal processes are important in understanding how fugacity changes with pressure at constant temperature.
53. What is the significance of isothermal processes in the study of critical phenomena?
Near the critical point of a substance, where the distinction between liquid and gas phases disappears, isothermal processes are crucial for understanding behavior. The critical isotherm, an isothermal process at the critical temperature, has unique properties.
54. How does the concept of isothermal processes apply to the behavior of quantum gases?
In the study of quantum gases, such as Bose-Einstein condensates, isothermal processes are important for understanding phase transitions and other phenomena that occur at extremely low temperatures.
55. What is the relationship between isothermal processes and the Helmholtz free energy?
The Helmholtz free energy (A = U - TS) is particularly useful for analyzing isothermal processes. In an isothermal process, the change in Helmholtz free energy equals the negative of the work done by the system.
56. How do isothermal processes relate to the concept of chemical potential?
Chemical potential, which describes how the energy of a system changes when particles are added or removed, is often studied under isothermal conditions. This is crucial in understanding phase equilibria and chemical reactions.
57. What is the significance of isothermal processes in the study of magnetic materials?
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.

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