Question

$3$ moles of an ideal monoatomic gas performs $A B C D A$ cyclic process as shown in figure below. The gas temperatures are $T_{A}=400\, K$, $T_{B}=800\, K ,\, T_{C}=2400\, K$ and $T_{D}=1200\, K$. The work done by the gas is (approximately) $(R=8.314\, J / mol\, K )$

• A. 10 kJ
• B. 20 kJ
• C. 40 kJ
• D. 100 kJ

Answer 1

Answer: (B)

Processes $A$ to $B$ and $C$ to $D$ are parts of straight line graphs of form $y=m x$.
Also, $p=\frac{\mu R}{V} T(\mu=3)$
$p \propto T$
So, volume remains constant for the graphs $A B$ and $C D$
So, no work is done during processes for $A$ to $B$ and $C$ to $D$.
$W_{A B}=W_{C D}=0$
and $W_{B C}=p_{2}\left(V_{C}-V_{B}\right)$
$=\mu R\left(T_{C}-T_{B}\right)$
$=3 R(2400-800)$
$=3 R \times 1600$
$=4800\, R$
$W_{D A} =p_{1}\left(V_{A}-V_{D}\right)$
$=\mu R\left(T_{A}-T_{D}\right)$
$=3 R(400-1200)$
$=-2400\, R$
Work done in complete cycle
$W =W_{A B}+W_{B C}+W_{C D}+W_{D A}$
$=0+4800 R+0+(-2400) R$
$=2400\, R$
$=19.944\, J =20\, kJ$