03/12/2025
THE ADIABATIC PROCESS
An adiabatic process is a thermodynamic process in which there is no heat exchange between a system and its surroundings. The system is thermally isolated. The process is carried out so rapidly that heat exchange is impossible within a short period
Examples
In a pneumatic tire, heat is generated rapidly when the gas is compressed.
Vertical airflow in the atmosphere – Hot air rises and rapidly cools down
Expansion and contraction of interstellar gas
Certain parts of the Carnot engine and Diesel engine are adiabatic.
Gas turbines operating on the Otto cycle and Brayton cycle use adiabatic processes.
ADIABATIC PROCESS, FIRST LAW OF THERMODYNAMICS, AND ENTHALPY CHANGE
The first law of thermodynamics establishes a relationship between the internal energy (ΔU) of a system, heat transfer (Q), and work done (W). The following equation represents the first law.
ΔU = Q – W
Since there is no exchange of heat, Q = 0, and the work done is given by
W = – ΔU
It means that if a system does work, energy leaves the system. The work done equals the internal energy change.
The opposite also holds correct. If the surrounding does work on the system, energy enters the latter.
W = ΔU
The first law of thermodynamics in terms of enthalpy change is given by
ΔH = ΔQ + VΔP
For an adiabatic process
ΔH = VΔP
Therefore, the enthalpy change is equal to the flow process work done by the system. This equation applies to open-flow systems like a turbine or pump.
WORK DONE IN AN ADIABATIC PROCESS
Introduction
An adiabatic process is a thermodynamic process in which there is no heat transfer between the system and its surroundings. This means that the heat transfer (Q) is zero, and the change in internal energy (ΔU) is equal to the work done (W).
Work Done Formula
The work done (W) in an adiabatic process is given by:
W = (p1V1 - p2V2) / (γ - 1)
where:
p1, V1 = initial pressure and volume
p2, V2 = final pressure and volume
γ = adiabatic index (Cp / Cv)
Derivation
The first law of thermodynamics states that:
ΔU = Q - W
Since Q = 0 for an adiabatic process, we have:
ΔU = -W
The internal energy (U) of an ideal gas is a function of temperature only, so we can write:
ΔU = nCvΔT
where n is the number of moles of gas, and Cv is the specific heat capacity at constant volume.
Equating the two expressions for ΔU, we get:
nCvΔT = -W
Using the ideal gas equation, we can write:
pV = nRT
Substituting this into the expression for W, we get:
W = (p1V1 - p2V2) / (γ - 1)
Alternative Formula
Using the ideal gas equation, the work done can also be expressed as:
W = nR(T1 - T2) / (γ - 1)
where:
n = number of moles of gas
R = gas constant
T1, T2 = initial and final temperatures
Example
A gas is compressed adiabatically from an initial volume of 1 m³ to a final volume of 0.5 m³. The initial pressure is 100 kPa, and the adiabatic index is 1.4. Find the work done.
Solution:
p1V1^γ = p2V2^γ
p2 = p1(V1/V2)^γ = 100 kPa(1/0.5)^1.4 = 264 kPa
W = (p1V1 - p2V2) / (γ - 1) = (100 kPa x 1 m³ - 264 kPa x 0.5 m³) / (1.4 - 1) = 70 kJ
Adiabatic Index (γ)
The adiabatic index (γ) is the ratio of the specific heat capacity at constant pressure (Cp) to the specific heat capacity at constant volume (Cv).
γ = Cp / Cv
The value of γ depends on the type of gas:
- Monatomic gas: γ = 5/3
- Diatomic gas: γ = 7/5
- Polyatomic gas: γ = 4/3
Applications
Adiabatic processes are important in many engineering applications, including:
- Internal combustion engines
- Gas turbines
- Refrigeration systems
- Air compressors
