Question

For an adiabatic expansion of a perfect gas the volume of ΔP/P is equal to - 
1. \(\dfrac{\Delta V}{V}\)
2. \(\gamma \dfrac{\Delta V}{V}\)
3. \(-\gamma \dfrac{\Delta V}{V}\)
4. \(-\gamma^2 \dfrac{\Delta V}{V}\)

Answer 1

Correct Answer - Option 3 : \(-\gamma \dfrac{\Delta V}{V}\)

Concept:

Adiabatic process: It is a process in which there is no heat interaction between the system and surroundings.

The adiabatic expansion of a perfect gas is governed by the equation

PV^γ = Constant;

In general, if Z = (A^p B^q)/C^r;

The relative error of Z is given by 

\(\frac {\Delta Z}{Z} = p \frac {\Delta A}{A} + p \frac {\Delta A}{A} + r \frac {\Delta C}{C}\)

Calculation:

Given adiabatic expansion ⇒ PV^γ = Constant

\(\Rightarrow \frac {\Delta P}{P} + \gamma \frac {\Delta V}{V} = 0\)

\(\Rightarrow \frac {\Delta P}{P} = - \gamma \frac {\Delta V}{V} \)