Question

A sample of gas at temperature $T$ is adiabatically expanded to double its volume. The work done by the gas in the process is $\left(\right.$ given, $\left.\gamma=\frac{3}{2}\right)$ :

• A. $W=T R[\sqrt{2}-2]$
• B. $W=\frac{R}{T}[2-\sqrt{2}]$
• C. $W=R T[2-\sqrt{2}]$
• D. $W=\frac{T}{R}[\sqrt{2}-2]$

Answer 1

Answer: (C)

$ T_1 V_1^{\gamma-1}=T_2 V_2^{\gamma-1}$
$ T V^{1 / 2}=T_2(2 V)^{1 / 2} $
$ T_2=\frac{T}{\sqrt{2}} $
$ W=\frac{R\left(T_1-T_2\right)}{\gamma-1}=\frac{R\left(T-\frac{T}{\sqrt{2}}\right)}{\frac{1}{2}}=R T(2-\sqrt{2})$