Question

The amount of work done in an adiabatic expansion from temperature $T$ to $T_{1}$ is

• A. $n R\left(T-T_{1}\right)$
• B. $n \frac{R}{\gamma-1}\left(T-T_{1}\right)$
• C. $n R T$
• D. $n R\left(T-T_{1}\right)(\gamma-1)$

Answer 1

Answer: (B)

$\Delta Q=\Delta U+\Delta W$, but $\Delta Q=0$ for adiabatic process.
$\Rightarrow \Delta W=-\Delta U=-n C_{\nu}\left(T_{1}-T\right)=\frac{n R\left(T-T_{1}\right)}{\gamma-1}$