Q. Which of the following is true in the case of an adiabatic process, where $\gamma = C_{p}/C_{v}?$
A) $p^{1 - \gamma}T^{\gamma} = constant$
B) $p^{\gamma}T^{1 - \gamma} = constant$
C) $pT^{\gamma} = constant$
D) $p^{\gamma}T = constant$
Explanation
(a) For adiabatic change equation of state is
$pV^{\gamma} = constant$
It can also be re-written as
$TV^{\gamma - 1} = constant\ \left\lbrack as\ p = \frac{nRT}{V} \right\rbrack$
and $p^{1 - \gamma}T^{\gamma} = constant\left\lbrack as\ V = \frac{nRT}{P} \right\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.