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 (given, $\gamma=\frac{3}{2}$)

• 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)

$W=R T[2-\sqrt{2}]$

Answer 2

T1​V1γ−1​=T2​V2γ−1​
TV1/2=T2​(2V)1/2
T2​=2​T​
W=γ−1R(T1​−T2​)​=21​R(T−2​T​)​=RT(2−2​)