Question

One mole of an ideal gas at a temperature $T_{1} K$ expands slowly according to the law $\frac{p}{V}=$ constant. Its final temperature is $T_{2} K .$ The work done by the gas is

• A. $R\left(T_{2}-T_{1}\right)$
• B. $2 R\left(T_{2}-T_{1}\right)$
• C. $\frac{R}{2}\left(T_{2}-T_{1}\right)$
• D. $\frac{2 R}{3}\left(T_{2}-T_{1}\right)$

Answer 1

Answer: (C)

$P V^{-1}=C$
Comparing $P V^{N}=C$
$N=-1$
$W=\frac{n R\left(T_{1}-T_{2}\right)}{N-1}=$
$\frac{1 \times R\left(T_{1}-T_{2}\right)}{-2}$
$W=\frac{R\left(T_{2}-T_{1}\right)}{2}$