Adiabatic Process

Adiabatic Process is a thermodynamic process in which there is no heat exchange between the system and the environment. It means the energy of the system remains unchanged with time. For Example, the water inside a thermo steel bottle that remains hot is one of the best real-life examples of the Adiabatic Process.

In this article, we will learn what the is Adiabatic Process, its definition, example, and equation to explain the process and its graphical representation. We will also solve some numerical based on the adiabatic process and see the previous year’s questions of competitive exams.

Adiabatic Process

What is Adiabatic Process?

Adiabatic Process is a thermodynamic change in a system where no heat is exchanged with its surroundings. It is a quick and efficient transformation that happens without any heat coming in or going out. Adiabatic processes commonly occur in gases and are characterized by their swift nature, often taking place too rapidly for any significant change to happen.

Adiabatic Process Definition

The thermodynamic process in which there is no exchange of heat from the system to the surrounding or from the surrounding into the system is called Adiabatic Process.

Adiabatic Process Example

Think about the example of a Thermosteel Bottle, thermos don’t need any help from the surroundings to keep the tea hot, like this adiabatic processes are silently at play. So in adiabatic process heat transfer from the system or into the system is prevented by either isolating the system from its environment, or by carrying out the change so rapidly that there is no time for any exchange of heat. Adiabatic process can be reversible or irreversible in nature. Puncturing an inflated balloon or tyre are examples of adiabatic processes.

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P-V Diagram for Adiabatic Process

PV Diagram for Adiabatic Process shows the graph of Adiabatic Process by plotting the relation between Pressure and Volume of the system. As shown in the below diagram, when volume increases the pressure of the system goes on decreasing similarly if volume decreases the pressure will increase. The P-V graph of adiabatic process is steeper than that of isothermal process, so it indicates that the temperature of the system changes more rapidly, hence there is no heat exchange occurs between system and surrounding.

PV Diagram for Adiabatic Process

Thermodynamics of Adiabatic Process

In adiabatic process , the heat exchange is zero so using first law of thermodynamics we can derive an equation for adiabatic process as described below. In adiabatic process temperature of system also changes .

• When a system expands adiabatically, W is positive (i.e. work is done by the system) and the internal energy of the system decreases.
• When a system is compressed adiabatically, W is negative (i.e. work is done on the system ) and the internal energy of the system increases.

Adiabatic Process Formula

Adiabatic process can be represented thermodynamically as,

PV^γ = C = Constant

where

• P is the Pressure of System
• V is the Volume of System
• γ is Adiabatic Ratio

So this formula tells us that if pressure of system increases ,volume decreases and vice versa.

Adiabatic Process Formula Derivation

According to First Law of Thermodyanmcs,

ΔU = ΔQ −ΔW

As ΔQ = 0 in adiabatic process so,

ΔU = −W

For an ideal gas, the internal energy ΔU is related to temperature ΔT through the equation U=nCvT, where n is the number of moles and Cv is the molar specific heat at constant volume. Also, the work done by the gas in expanding against an external pressure is given by

W = −PΔV

Substituting these values in above equation we get

nC_vΔT = PΔV

For an adiabatic process, the relation between pressure, volume, and temperature for an ideal gas can be derived by using the ideal gas law PV = nRT and the specific heat ratio γ:

PV^γ = constant

For an Adiabatic process we have an equation between pressure (P) and volume (V) as,

PV^γ = constant =C

Where γ is the ratio of specific heat at constant pressure to specific heat at constant volume , is is also called as adiabatic ratio.

Value of γ is 5/3 for monoatomic gases, 7/5 for diatomic gases and 4/3 for triatomic gases.

Work done in Adiabatic Process

Work done in adiabatic process is dependent on initial and final pressure, initial and final volumes of system and adiabatic ratio.

• During adiabatic compression, the work is done on the system and is considered positive. The energy is transferred to the system, increasing its internal energy.
• During adiabatic expansion, the work is done by the system and is considered negative. The energy is transferred from the system, decreasing the internal energy of the system.

Work done in adiabatic process is given as,

W= (P_fV_f – P_iV_i) / (1 – γ)

where,

• P_f and V_f are final pressure and final volume of system respectively
• P_i and V_i are initial pressure and initial volume of system respectively
• γ is Adiabatic Ratio

Adiabatic Index

Adiabatic index is also known as adiabatic ratio, and adiabatic index is defined as the ratio specific heat at constant pressure to specific heat at constant volume.

So Adiabatic Index is given as

γ = C_p/C_v

where,

• γ is Adiabatic Index
• C_p is Specific Heat at Constant Pressure
• C_v is Specific Heat at Constant Volume

Note:

• In adiabatic process, heat exchange is zero but temperature change is not zero i.e. temperature of system changes in adiabatic process.
• Adiabatic expansion causes cooling up of system and adiabatic compression causes heating up of the system.
• In most of the times, an adiabatic change is a sudden change. During a sudden change the system does not find any time to exchange heat with its surrounding.

Adiabatic Process Application

Have a look on below applications to understand the adiabatic process happening in dailly life .

• Cooling of Spray Can: Have you ever used a spray can and felt it get cold in your hand? The rapid expansion of the gas inside the can as you release the spray causes adiabatic cooling. The gas expands quickly, and because it happens without heat exchange, the temperature drops, making the can feel cold.

• Bicycle Pump: When you use a bicycle pump, you might notice that the pump gets warm after a while. The air inside the pump undergoes adiabatic compression as you pump it into the tire. The rapid compression causes the air to heat up, and since the process is quick, there’s little time for heat exchange with the surroundings.

• Hiking in High Altitudes: If you’ve been on a mountain hike, you might have noticed the air getting cooler as you ascend. As you climb higher, the air pressure decreases, and the air expands adiabatically, leading to a drop in temperature. This is why mountain areas tend to be cooler, even on a sunny day.

Reversible Adiabatic Process

A reversible adiabatic process is when a system changes its state without exchanging heat with the surroundings, and the changes are reversible, meaning it can go back and forth without any energy loss as heat. This process occurs without any external influence and is characterized by a rapid, frictionless, and perfectly efficient transformation.

Example of Reversible Adiabatic Process is expansion of steam in steam turbines and gas in gas turbines.

Difference between Adiabatic Process and Isothermal Process

The difference between Adiabatic Process and Isothermal Process is tabulated below:

Adiabatic Process vs Isothermal Process
Isothermal Process	Adiabatic process
The thermodynamic process in which temperature of system remains constant throughout the process is called isothermal process.	The thermodynamic process in which there is no exchange of heat from system to surrounding or from surrounding into system is called as adiabatic process .
Heat transfer is allowed.	No heat transfer from or into the system.
The temperature of system remains constant.	The temperature of system changes due to internal energy changes.
The pressure is more at given volume of system	The pressure is less at a given volume of system
Specific heat becomes infinite	Specific heat becomes zero
Examples: Reversible expansion or compression in a perfectly conducting cylinder.	Examples: Non-reversible processes like the compression stroke in a car engine.

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Adiabatic Process – Solved Examples

Example 1: A gas (γ = 1.4) of 2m³ Volume and at a pressure of 2×10⁵ N/m² is compressed adiabatically to a volume 5 m ³. Find its new pressure.

Solution:

In adiabatic process, we have PV^γ = Constant

So using this equation we can write P₁V₁^γ=P₂V₂^γ

Given,

• P₁ = 2⨯10⁵
• V₁= 2m³
• V₂ = 5m³

P₂ = ?

(2⨯10⁵)⨯(2)^1.4 = P₂⨯(5)^1.4

2⨯10⁵⨯(2/5)^1.4 = 5⨯P₂

P₂ = 5.54⨯10⁴

hence P₂=5.54⨯10⁴ N/m²

So the new pressure of gas is 5.54⨯10⁴ N/m².

Example 2: In an adiabatic expansion of gas, the change in internal energy is -50 J, what is the work done in this process?

Solution:

According to the first law of thermodynamics,

ΔQ = ΔU + ΔW

So in adiabatic process , heat transfer is zero so ΔQ=0

Given that ΔU = 50 J

using first law of thermodynamics

0 = 50 + ΔW

ΔW =-50 J

Hence work done in this process is -50 J.

Example 3: What will be the ratio of final volume to initial volume of of a gas if it is compressed adiabatically till its temperature becomes twice of initial temperature.

Solution:

T₁V₁^(γ-1)=T₂V₂^(γ-1)

V₂/V₁ = (T₁/T₂)^(1/(γ-1))

V₂/V₁ = (1/2)^(1/(γ-1))

V₂/V₁ < 1/2 (because γ>1)

Example 4: A gas is compressed adiabatically by a force of 600 N acting through a distance of 5.0 cm. The net change in its internal energy is

Solution:

ΔW = -600⨯5⨯10 ^-2 = -30 J

For an adiabatic process

ΔQ = ΔW+ΔU

ΔQ = 0

So ΔU = -ΔW

Hence ΔU = 30 J

Adiabatic Process – JEE Questions

Q1. During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio C_P/C_V for the gas is

1. 4/3
2. 2
3. 5/3
4. 3/2

Solution:

Option (4) 3/2 is correct

In an adiabatic process

Tγ = kP(γ-1)

T(γ/γ-1) = kP

Given T₃ = kP

hence γ/γ-1 = 3;

3γ-3 = γ

γ = 3/2

C_P/C_V = 3/2

Q2. During an adiabatic compression of gas, its temperature

1. Falls
2. Rises
3. Remains Constant
4. Becomes Zero

Solution:

Option (2) Rises is correct

During adiabatic compression of gas, volume decreases hence pressure increases and as a result temperature of gas increases.

Adiabatic Process – Practice Questions

1. The adiabatic bulk modulus of perfect gas under constant pressure is given by

1. P
2. 2P
3. P/2
4. γP

2. Volume of a gas is reduced to 1/4 of its initial volume adiabatically at 27 ℃ , The final temperature of gas will be?

3. Amount of work done in an adiabatic expansion from temperature T to T₁ is?

4. One gm-mol of a diatomic gas (γ = 1.4) is compressed adiabatically , so that its temperature rises from 27 ℃ to 127 ℃ . The work done will be

5. During the adiabatic expansion of 2 mole of a gas, the internal energy of a gas is found to be decrease by 2 joule, the work done during the process on the gas will be?

Adiabatic Process – FAQs

1. What is Meaning of Adiabatic Process?

The thermodynamic process in which there is no exchange of heat from system to surrounding or from surrounding into system is called as adiabatic process .

2. What Remains Constant in Adiabatic Process ?

In adiabatic process, the total heat of the system remains constant because in adiabatic processes there is no heat exchange from or to the system .

3. What is Relation between Pressure and Volume of System in Adiabatic Process ?

In adiabatic process, the relation between pressure (P) and volume (V) of the system is given as PV^γ= constant = C

4. What is Difference between Adiabatic Process and Isothermal Process?

In isothermal process the temperature of the system remains constant while in the adiabatic process there is no exchange of heat between System and Surrounding

5. What is Zero in Adiabatic Process?

In Adiabatic Process, the net change in the internal energy of the system remains zero

6. What are Four Thermodynaomic Processes?

The four Thermodynamic Processes are Isothermal Process, Adiabatic Process, Isobaric Process and Isochoric Process

7. What is Adiabatic Process Equation?

Adiabatic Process Equation is given as PV^γ = Constant where γ = C_p/C_v