Q. Initially two gas samples 1 and 2 are at the same condition. The volume of the two are halved, one isothermally and the other adiabatically. What is the relation between the final pressure $p_{1}and\ p_{2}?$
A) $p_{1} = p_{2}$
B) $p_{1} > p_{2}$
C) $p_{2} > p_{1}$
D) Cannot be determined
Explanation
(c) For isothermal process
$p_{1}V = K$ (constant)
$p_{1} = \frac{K}{V}$ ----(i)
$= \frac{K}{V/2} = 2K$
For adiabatic process
$P_{2}V^{\gamma} = K$ (constant)
$\therefore\ \ \ \ \ \ P_{2} = \frac{K}{V^{\gamma}}$ ----(ii)
$= \frac{K}{\left( \frac{V}{2} \right)^{\gamma}} = K(2^{\gamma})$
From Eqs. (i) and (ii), we have
$P_{2} > P_{1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.