Adiabatic Process Formula Derivation
According to First Law of Thermodynamics,
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
nCvΔT = 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:
PVγ = constant
For an Adiabatic process we have an equation between pressure (P) and volume (V) as,
PVγ = 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.
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