Question

$5.6$ liter of Helium gas at $STP$ is adiabatically compressed to $0.7$ liter. Taking the initial temperature to be $T_{1},$ then work done on the system in the process is (no. of moles $=1$ )

• A. $\frac{9}{8}RT_{1}$
• B. $\frac{3}{2}RT_{1}$
• C. $\frac{15}{8}RT_{1}$
• D. $\frac{9}{2}RT_{1}$

Answer 1

Answer: (D)

$T_{1}V_{1}^{\gamma - 1}=T_{2}V_{2}^{\gamma - 1}$
$T_{i}\cdot V^{7 / 5 - 1}=T_{2}\cdot \left(\frac{1}{32} V\right)^{7 / 5 - 1}$
$T_{2}=4T_{i}=αT_{i}$
$\alpha =4$