Q. Ideal gas undergoes an adiabatic change in its state from $\left( p_{1}V_{1}T_{1} \right)to\ \left( p_{2},\ V_{2},\ T_{2} \right).$ The work done (W) in the process is ($\mu$=number of molecules, $C_{p}and\ C_{v}$are molar specific heats of gas)
A) $W = \mu C_{p}(T_{1} - T_{2})$
B) $W = \mu C_{v}\left( T_{1} - T_{2} \right)$
C) $W = \mu C_{p}(T_{1} + T_{2})$
D) $W = \mu C_{v}(T_{1} + T_{2})$
Explanation
(a) In adiabatic change work done
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ W = \mu C_{V}\Delta T$
or $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ W = \mu C_{V}(T_{1} - T_{2})$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.