Q. One mole of an ideal gas expands adiabatically from an initial temperature $T_{1}$ to a final temperature $T_{2}$.The work done by the gas would be
A) $\left( C_{p} - C_{v} \right)(T_{1} - T_{2})$
B) $C_{p}(T_{1} - T_{2})$
C) $C_{v}(T_{1} - T_{2})$
D) $\left( C_{p} - C_{v} \right)(T_{1} + T_{2})$
Explanation
(c) $dW = dU = \mu C_{v}\mathrm{\Delta}T = - C_{v}\left( T_{2} - T_{1} \right) = C_{v}(T_{1} - T_{2})$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.