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

An adiabatic process is a thermodynamic process in which no heat is exchanged between a system and its surroundings. Instead, any change in the system's internal energy results from work done by or on the system. This concept is essential in physics and engineering, particularly in understanding the behaviour of gases. For example, when a gas is compressed rapidly, its temperature rises, even though no heat is added — a phenomenon explained by the adiabatic process.

A real-life example of this can be observed in a bicycle pump. As you compress the air inside the pump quickly, the air becomes warmer. Since there’s no time for heat to escape, the compression process is adiabatic. Similarly, adiabatic cooling occurs when air rises in the atmosphere, expands, and cools without exchanging heat, which plays a crucial role in weather patterns and cloud formation.

What is the Adiabatic Process?

Adiabatic meaning: There is no heat exchange in a thermodynamic process Neither during an adiabatic process 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 is a change in internal energy.
ΔU=−ΔW
If ΔW= positive then ΔU become negative so temperature decreases ie., adiabatic expansion produces cooling.
If ΔW= negative then ΔU become positive so temperature increases ie., adiabatic compression produces heating.

Adiabatic Process Formula

In terms of adiabatic processes, the following equation applies:

PV ^γ = constant

Then,

The pressure in the system is P

A system's volume is V

γ relates heat capacity at constant pressure C_p to heat capacity at constant volume C_V

Work done in the adiabatic process

W=∫ViVfPdV=∫ViVfKVγdV⇒W=[PiVi−PfVf](γ−1)=μR(Ti−Tf)(γ−1)

Adiabatic Expansion

A closed system with constant pressure and diminishing temperature exhibits an ideal behaviour known as adiabatically expanding.

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.

Heating and Cooling by adiabatic motion

An increase in temperature is caused by adiabatically compressing a gas. The temperature drops as a result of adiabatic expansion, or a spring. 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 vapour 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.

Adiabatic Process Example

Describe the Difference Between An Isothermal and An Adiabatic Process

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

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Solved Examples Based on Adiabatic Process

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

1) monoatomic

2) diatomic

3) triatomic

4) a mixture of monoatomic and diatomic.

Solution:

Adiabatic Process

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

wherein
ΔQ=0

and
Work done in Adiabatic process

W=∫PdV

wherein

W=nR(Ti−Tf)γ−1

γ= adiabatic exponent
For adiabatic process
W= Change in internal energy =nCv(Ti−Tf) or, 146×103=(1000)×Rγ−1×7
146=8.3×7γ−1
or, γγ−1=58.1146
or, γ=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:

Condition of Adiabatic Process

1) There should not be any exchange of heat between the system and surroundings.

2) The system should be compressed or expand suddenly.

No process is perfectly adiabatic e.g. sudden burst of a tyre.
ΔQ=ΔU+ΔW=0ΔW=−ΔU
If ΔW is positive i.e gas does work, then ΔU should be negative meaning internal energy is used in doing work

Hence, the answer is the option 2.

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 Adiabatic Process )
ΔU+ΔW=0
By the first law of thermodynamic

ΔQ=ΔU+ΔW
For the adiabatic process, there is no exchange of heat b/w the system and the surrounding

i.e ΔQ=0
So ΔU+ΔW=0

ΔW=−ΔU

Work done by the system equals to decrease in internal energy

Hence, the answer is the 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:

In the given question
P∝T3

or PT−3= constant
From adiabatic equation

P1−γ⋅Tγ= constant
From equation 1 and 2

γ1−γ=−3 or 3γ−3=γ or γ=3/2
∴CpCv=γ=3/2

Hence, the answer is the option (4).

Example 5: Two moles of an ideal monoatomic gas occupy a volume V at 27^oC. 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:

Equation of state
dQ=0nCVdT+PdV=0

wherein
On solving

γdVV+dPP=0⇒PVγ=constant
For Adiabatic process

T1V1γ−1=T2V2γ−1(γ=53)300(v)2/3=T2(2v)2/3or T2=30022/3≃189KΔU=f2(nRΔT)=32×2×253×(189−300)5ΔU=f2(nRΔT)=32×2×253×(189−300)5=−2.7kJ

Hence, the answer is the option 4.

Summary

To ensure that everyone has a comprehensive understanding of the adiabatic process and the work it accomplishes, both the notion of the adiabatic process and the derivation of its work are explained. It is discussed how adiabatic processes cause compression and expansion; in compression, no heat is generated or lost, and in expansion, there is no heat exchange with the environment. You will benefit greatly from this article in your academic endeavours.