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