Careers360 Logo
Scan and Download the App!
Search Faster,
Smarter, Better
Rated 4.2
by 1M+ students
Adiabatic Process - Meaning, Equation, Formula, Example, FAQs

Adiabatic Process - Meaning, Equation, Formula, Example, FAQs

Edited By Vishal kumar | Updated on Jul 22, 2025 09:03 AM IST

When there is no exchange of heat between the system and the surroundings, the process is known as adiabatic process. It is an integral part of thermodynamics. The concept of adiabatic process is a fundamental principle in physics which deals with the behaviour of gases.

By understanding the concept of the adiabatic process, students get an idea about work, heat, and internal energy. This article provides insight on important topics like what is an adiabatic process, the work done by an adiabatic process derivation, daily life examples of adiabatic processes, adiabatic expansion and compression, and types of adiabatic processes.

This Story also Contains
  1. What is an Adiabatic Process in Thermodynamics?
  2. Work Done By Adiabatic Process Derivation
  3. Types Of Adiabatic Processes
  4. PV Diagram Of Adiabatic Process: Work Done
  5. Adiabatic Process Examples In the Real World
  6. Difference Between Isothermal and Adiabatic Process
  7. Solved Examples Based on Adiabatic Process
Adiabatic Process - Meaning, Equation, Formula, Example, FAQs
Adiabatic Process - Meaning, Equation, Formula, Example, FAQs

What is an Adiabatic Process in Thermodynamics?

Define adiabatic process: There is no heat exchange in an adiabatic process in thermodynamics, neither during an adiabatic expansion nor compression. An adiabatic process is one in which, both irreversibility and reversibility are possible. The following conditions must be met for an adiabatic reaction to occur:
Insulation must be perfect between the system and its surroundings. It is important to carry out the process rapidly. The turbines are great examples of adiabatic systems. During the adiabatic process, the work done changes internal energy.
ΔU=ΔW
If ΔW= positive then ΔU becomes negative so temperature decreases ie., adiabatic expansion produces cooling.
If ΔW= negative then ΔU becomes positive so temperature increases ie., adiabatic compression produces heating.

Work Done By Adiabatic Process Derivation

In terms of adiabatic processes, the following equation applies:

PVγ= constant ( adiabatic process formula)

where,

  • The pressure in the system is P
  • A system's volume is V

According to the first law of thermodynamics,

ΔU=Q+W

For adiabatic process,

ΔU=W (there is no heat exchange, Q=0)

Let W work be done as the system goes from initial state P1 V1 T1 to final state P2 V2 T2.

Work Done, W=V1V2PdV .............(1)

Using the adiabatic process formula, PVγ= constant in the above equation we get

Wadia=V1V2 constant VγdV

W= constant V1V2VγdV

By integrating both sides

Wadia=11γ[ constant V2γ1 constant V1γ1]

We know that, constant =P1V1γ=P2V2γ

Wadia =11γ[PfVfγVfγ1PiViγViγ1]

Simplifying we get,

Wadia=1γ1(P1V1P2V2) ....................(2)

Using ideal gas, P2V2=nRT2 and P1V1=nRT1

Substituting in (2), we get

Wadia=nRγ1(T1T2)

where,

  • R is the universal gas constant
  • T1 and T2 are the temperatures in initial and final states respectively.
NEET Highest Scoring Chapters & Topics
This ebook serves as a valuable study guide for NEET exams, specifically designed to assist students in light of recent changes and the removal of certain topics from the NEET exam.
Download E-book

This is the work done by the adiabatic process equation.

Adiabatic Expansion

  • A closed system with constant pressure and diminishing temperature exhibits an ideal behavior known as adiabatically expanding. The gas loses energy to do the work.
  • Since the gas does work on the surroundings in adiabatic expansion, W>0 ( work done is positive)

Adiabatic Compression

  • Adiabatic compression of air is defined as one where there is no heat exchange between the air and the compression compressor and the internal energy of the air is increased in proportion to the external work done in an adiabatic process on it. Since the temperature rises during an adiabatic process compression, the pressure of air is greater than the volume.
  • Since the surrounding does work on gas W<0 ( work done is negative).

Heating And Cooling By Adiabatic Motion

Adiabatic compression causes a gas to increase in temperature, while adiabatic expansion, or a spring, causes the temperature to drop. An ideal gas, however, expands with isothermal heat.

In many practical situations, heat conduction through walls can be slow compared to the compression time of gas, because a piston compressing a gas contained inside a cylinder increases its pressure.

Generally, diesel engines make use of this to ignite the fuel vapor when there is little heat dissipation during an adiabatic process a compression stroke.

An adiabatically isolated system is cooled by decreasing the pressure on it, which allows it to expand and change its environment.

Types Of Adiabatic Processes

(i) Reversible Adiabatic Process

  • It occurs infinitely slowly
  • ΔS=0
  • Frictionless
  • Example: thermodynamic process in Carnot engine

(ii) Irreversible Adiabatic Process

  • Sudden change in pressure or volume
  • ΔS>0
  • Friction is present
  • Example: Rapid compression of gas

PV Diagram Of Adiabatic Process: Work Done

The area under the PV diagram of the adiabatic process gives the work done by the adiabatic process. The curve of the adiabatic process is steeper than that of the isothermal process.

PV Diagram Of Adiabatic Process

Adiabatic Process Examples In the Real World

Examples of adiabatic processes include:

  1. The diesel engine's fast adiabatic compression helps ignite the fuel by raising the air's temperature.
  2. Adiabatic expansion of air results in cloud formation and precipitation.
  3. Adiabatic expansion leads to the rising of the hot air balloon and adiabatic compression leads to descending of the hot air balloon.
  4. A piston cylinder can be used for expanding or compressing gas adiabatically.
  5. Sound waves in gases undergo an adiabatic process.

Difference Between Isothermal and Adiabatic Process

The isothermal versus adiabatic process is explained in the table below:

Isothermal process

Adiabatic process

An isothermal process is defined as one of the thermodynamic processes which occur at constant temperature.

An adiabatic process is defined as one of the thermodynamic processes that occur without any heat transfer between the system and the surroundings.

Work done in an adiabatic process is due to the change in the net heat content in the system.

Work done in the adiabatic process is due to the change in its internal energy.

The temperature cannot be varied

The temperature can be varied

There is a transfer of heat

There is no transfer of heat

Also See,

Thermodynamic State Variables And Equation Of State

Heat, Internal Energy And Work - Thermodynamics

First Law Of Thermodynamics

Cyclic and Non cyclic process

Isobaric Process

Isochoric Process

Isothermal Process

Solved Examples Based on Adiabatic Process

Example 1: The work of 146 kJ is performed to compress one kilomole of gas adiabatically and in this process, the temperature of the gas increases by 7C. The gas is (R=8.3 J mol1 K1)

1) monoatomic

2) diatomic

3) triatomic

4) a mixture of monoatomic and diatomic.

Solution:

Adiabatic Process

When a Thermodynamic System changes in such a way that no exchange of heat takes place.

1. Work Done Formula: W=nRTiTfγ1
2. Plug in Values: 146,000=1000×8.3×7γ1
3. Compute Numerator: 58,100=1000×8.3×7
4. Solve for γ1:γ1=58,100146,000γ10.3986
5. Find γ:γ=1+0.3986γ1.4

Therefore, the corrected value of γ is approximately 1.4.

Hence, the answer is the option (2).

Example 2: When a gas expands adiabatically

1) The system should allowed to expand slowly

2) Internal energy of gas is used in doing work

3) The law of conservation of energy does not hold

4) No energy is required for expansion

Solution:

1. No Heat Exchange: In an adiabatic process, there should be no exchange of heat between the system and surroundings, meaning ΔQ=0.
2. Sudden Compression or Expansion: For a process to be approximately adiabatic, it should occur quickly. This rapid change ensures that there is no time for heat to transfer, as in the case of a sudden burst of a tire.

Since ΔQ=0, the first law of thermodynamics simplifies to:

ΔQ=ΔU+ΔW=0

or

ΔW=ΔU

This means that if ΔW (work done by the gas) is positive, then ΔU (change in internal energy) must be negative, indicating that the gas's internal energy is used to perform work.

Example 3: A given system undergoes a change in which the work done by the system equals the decrease in its internal energy. The system must have undergone an

1) Isothermal change
2) Adiabatic change
3) Isobaric change
4) Isochoric change

Solution:

In an adiabatic process:

ΔU+ΔW=0

According to the first law of thermodynamics:

ΔQ=ΔU+ΔW

For an adiabatic process, there is no exchange of heat between the system and its surroundings.

 i.e., ΔQ=0

So, ΔU+ΔW=0

ΔW=ΔU

This means the work done by the system equals the decrease in internal energy.

Hence, the answer is option 2.

Example 4: During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio CP/CV for the gas is

1) 4/3
2) 2
3) 5/3
4) 3/2

Solution:

PT3

or

PT3= constant 


From the adiabatic equation:

P1γTγ= constant 

Using equations (1) and (2), we can equate the powers of T and P :

γ1γ=3

Solving this, we get:

3γ3=γ

or

γ=32

Thus,

CpCv=γ=32

Hence, the answer is option (4).

Example 5: Two moles of an ideal monoatomic gas occupy a volume V at 27C. The gas expands adiabatically to a volume of 2 V .

Calculate (a) the final temperature of the gas and (b) the change in its internal energy.

  1. (a) 195 K (b) 2.7 kJ
  2. (a) 189 K (b) 2.7 kJ
  3. (a) 195 K (b) -2.7 kJ
  4. (a) 189 K (b) -2.7 kJ

Solution:

The equation of state for an adiabatic process is given by:

dQ=0nCVdT+PdV=0

On solving this, we find:

γdVV+dPP=0PVγ= constant 

For an adiabatic process, the relationship between temperature and volume is:

T1V1γ1=T2V2γ1

Given γ=53,T1=300K,V1=V, and V2=2V, we find T2 as follows:

300(V)23=T2(2V)23

or

T2=3001223189 K

Next, calculating the change in internal energy ΔU :

ΔU=f2(nRΔT)=32×2×253×(189300)

This simplifies to:

ΔU2.7 kJ
Hence, the answer is the option 4.

Frequently Asked Questions (FAQs)

1. When a process is adiabatically stable, which quantity remains constant?

When an adiabatic process occurs, the entire system's total heat remains constant.

2. What happens to the temperature of a gas during adiabatic compression?

During adiabatic compression, the temperature of a gas increases. This is because work is done on the gas, increasing its internal energy, and since no heat can escape (adiabatic), this energy increase manifests as a temperature rise.

3. What happens to the temperature of a gas during adiabatic expansion?

During adiabatic expansion, the temperature of a gas decreases. This is because the gas does work on its surroundings, decreasing its internal energy, and since no heat can enter (adiabatic), this energy decrease results in a temperature drop.

4. Can a real-world process be perfectly adiabatic?

In reality, no process can be perfectly adiabatic because some heat transfer is always present. However, processes that occur very quickly or in well-insulated systems can be approximated as adiabatic for practical purposes.

5. What is an example of an approximately adiabatic process in nature?

The compression and expansion of air in sound waves is an approximately adiabatic process. The pressure changes occur so rapidly that there's little time for heat transfer, making the process nearly adiabatic.

6. How does an adiabatic process differ from an isothermal process?

In an adiabatic process, no heat is exchanged with the surroundings, while temperature may change. In an isothermal process, temperature remains constant, but heat can be exchanged with the surroundings.

7. Can temperature change during an adiabatic process?

Yes, temperature can change during an adiabatic process. In fact, temperature usually does change because no heat is exchanged with the surroundings, so any work done by or on the system directly affects its internal energy and temperature.

8. How does the work done in an adiabatic process compare to an isothermal process?

For the same initial and final volumes, the work done in an adiabatic process is generally different from an isothermal process. In an adiabatic process, temperature changes, affecting the pressure-volume relationship, while in an isothermal process, temperature remains constant.

9. What is the relationship between pressure and volume in an adiabatic process?

In an adiabatic process, pressure and volume are related by the equation PV^γ = constant. This means that as volume decreases, pressure increases more rapidly than in an isothermal process (where PV = constant).

10. What is the significance of γ (gamma) in the adiabatic equation?

γ (gamma) is the heat capacity ratio (Cp/Cv) of the gas. It determines how much the temperature changes for a given pressure or volume change in an adiabatic process. A higher γ means a greater temperature change for the same volume change.

11. How does the work done in an adiabatic process depend on the initial and final states?

The work done in an adiabatic process depends only on the initial and final states of the system, not on the path taken between these states. This is because no heat is exchanged, so the change in internal energy is solely due to work.

12. What is the role of adiabatic processes in the Carnot cycle?

The Carnot cycle, which represents the most efficient possible heat engine, includes two adiabatic processes: adiabatic compression and adiabatic expansion. These processes connect the two isothermal processes in the cycle.

13. How does the efficiency of an adiabatic process compare to other thermodynamic processes?

Adiabatic processes can be more efficient than non-adiabatic processes in certain applications because they don't lose energy to heat transfer. This is why rapid compression or expansion in engines is often approximated as adiabatic.

14. How does an adiabatic process affect entropy?

In a reversible adiabatic process, entropy remains constant because no heat is exchanged with the surroundings. However, in an irreversible adiabatic process, entropy increases due to internal friction or other irreversibilities.

15. What is a polytropic process and how does it relate to an adiabatic process?

A polytropic process is a thermodynamic process that follows the equation PV^n = constant, where n is the polytropic index. An adiabatic process is a special case of a polytropic process where n = γ (the heat capacity ratio).

16. What is the first law of thermodynamics for an adiabatic process?

For an adiabatic process, the first law of thermodynamics simplifies to ΔU = -W, where ΔU is the change in internal energy and W is the work done by or on the system. This is because Q (heat transfer) is zero in an adiabatic process.

17. What is the equation for an adiabatic process involving an ideal gas?

The equation for an adiabatic process involving an ideal gas is PV^γ = constant, where P is pressure, V is volume, and γ (gamma) is the heat capacity ratio (Cp/Cv) of the gas.

18. How does an adiabatic process affect the internal energy of a system?

In an adiabatic process, the change in internal energy of the system is equal to the negative of the work done by or on the system. If work is done on the system, internal energy increases; if the system does work, internal energy decreases.

19. How does the adiabatic process relate to the operation of a refrigerator or heat pump?

In refrigerators and heat pumps, the rapid expansion of the refrigerant through the expansion valve is approximately adiabatic. This adiabatic expansion causes the refrigerant to cool, allowing it to absorb heat from the refrigerated space.

20. How does the adiabatic process relate to the operation of a diesel engine?

In a diesel engine, the initial compression of air in the cylinder is approximately adiabatic. This adiabatic compression raises the temperature of the air high enough to ignite the fuel when it's injected, without needing a spark.

21. How does the adiabatic process relate to the concept of enthalpy?

In an adiabatic process, there is no heat transfer (Q = 0), so the change in enthalpy (H) is equal to the work done (W) plus the change in internal energy (ΔU). For an ideal gas, the enthalpy change in an adiabatic process is solely due to the temperature change.

2nd Law Of Thermodynamics

02 Jul'25 08:10 PM

Thermodynamics Introduction

02 Jul'25 08:10 PM

Thermodynamic Equilibrium

02 Jul'25 07:49 PM

Polytropic Process

02 Jul'25 06:35 PM

Entropy

02 Jul'25 06:29 PM

Heat Engine

02 Jul'25 06:29 PM

Isochoric Process

02 Jul'25 06:29 PM

Isobaric Process

02 Jul'25 06:29 PM

First Law Of Thermodynamics

02 Jul'25 06:29 PM

Articles

Back to top