Q. In an adiabatic process, the state of a gas is changed from $p_{1},V_{1},T_{1}to\ p_{2},V_{2},T_{2}.$ Which of the following relation is correct?
A) $T_{1}V_{1}^{\gamma - 1} = T_{2}V_{2}^{\gamma - 1}$
B) $p_{1}V_{1}^{\gamma - 1} = p_{2}V_{2}^{\gamma - 1}$
C) $T_{1}p_{1}^{\gamma} = T_{2}V_{2}^{\gamma}$
D) $T_{1}V_{1}^{\gamma} = T_{2}V_{2}^{\gamma}$
Explanation
(a) For adiabatic process
${\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ P}_{1}\ V_{1}^{\gamma} = p_{2}V_{2}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{RT_{1}}{V_{1}}V_{1}^{\gamma} = \frac{RT_{2}}{V_{2}}V_{2}^{\gamma}$
${\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ T}_{1}V_{1}^{\gamma - 1} = T_{2}V_{2}^{\gamma - 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.