Question

$1$ mole of an ideal gas at $STP$ is subjected to a reversible adiabatic expansion to double its volume. The change in internal energy $(\gamma = 1.4)$

• A. $1169\,J$
• B. $769\,J$
• C. $1373\,J$
• D. $969\,J$

Answer 1

Answer: (C)

For adiabatic expansion
$T_{1}V_{1}^{\gamma-1} =T_{2}V_{2}^{\gamma-1}$
$T_{2} = T_{1}\left(\frac{V_{1}}{V_{2}}\right)^{\gamma-1} =273 \left(\frac{1}{2}\right)^{1.4-1}$
$\simeq 206\,K$
$dU=dW = \frac{R}{\gamma-1} \left(T_{1}-T_{2}\right)$
$=\frac{ 1\times8.31}{\left(1.4-1\right)}\left(273-206.89\right)$
$\simeq 1373\,J$