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 PVγ = Constant
So using this equation we can write P1V1γ=P2V2γ
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
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.
Table of Content
- What is Adiabatic Process?
- P-V Diagram for Adiabatic Process
- Thermodynamics of Adiabatic Process
- Adiabatic Process Formula
- Adiabatic Process Formula Derivation
- Work done in Adiabatic Process
- Adiabatic Index
- Adiabatic Process Application
- Reversible Adiabatic Process
- Difference between Adiabatic Process and Isothermal Process
- Adiabatic Process – Solved Examples
- Adiabatic Process – JEE Questions
- Adiabatic Process – Practice Questions