Question

$3$ moles of an ideal monoatomic gas perfoms a cycle shown in the figure. The gas temperature at $A,B,C,D$ are $T_A=400K,$ $T_B=800K,T_C=2400K,T_D=1200K.$ Find the work done by the gas.

• A. $12\text{kJ}$
• B. $20\text{kJ}$
• C. $120\text{kJ}$
• D. $24\text{kJ}$

Answer 1

The correct option is B $20\text{kJ}$

As process $AB,CD$ pass through origin on $P$ vs $T$ graphs, we can say that $P\propto T\Rightarrow V=\text{Constant}$.
Hence, Isochoric.
$W_{AB}=W_{CD}=0$

While process $BC,DA$ are isobaric in nature

$W_{BC}=3R(T_C-T_B)$
$W_{DA}=3R(T_A-T_D)$
$\therefore$ Total work done
$W_{AB}+W_{CD}+W_{BC}+W_{DA}=3R(T_A+T_C-T_B-T_D)$
$=3R(400+2400-800-1200)$
$=2400R=20\text{kJ}$