Thermodynamics Question 19

Question 19 - 01 February - Shift 1

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, $.\gamma=\frac{3}{2})$ :

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

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

(3) $W=\frac{R}{T}[2-\sqrt{2}]$

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

Show Answer

Answer: (4)

Solution:

Formula: Adiabatic process

$T_1 V_1^{\gamma-1}=T_2 V_2^{\gamma-1}$

$T V^{1 / 2}=T_2(2 V)^{1 / 2}$

$T_2=\frac{T}{\sqrt{2}}$

$W=\frac{R(T_1-T_2)}{\gamma-1}=\frac{R(T-\frac{T}{\sqrt{2}})}{\underline{1}}=R T(2-\sqrt{2})$