Question

Two moles of an ideal monoatomic gas undergo a cyclic process as shown in the figure. The temperatures in different states are given as $6 T_{1}=3 T_{2}=2 T_{4}=T_{3}=1800$ K. Determine the work done by the gas during the cycle.

• A. -1200 R
• B. 1200 R
• C. 1575 R
• D. -800 R

Answer 1

Answer: (A)

$6 T_{1}=3 T_{2}=2 T_{4}=T_{3}=1800\, K$
$T_{1}=300 K , T_{2}=600\, K$
$T_{4}=900 K , T_{3}=1800\, K$
$1 \rightarrow 4$ and $2 \rightarrow 3$ are isochoric process
work done $=0$
$W_{12} =P\left(V_{2}-V_{1}\right)=n R\left(T_{2}-T_{1}\right)$
$=2 \times R(600-300)=600\, R$
$W_{341} =P\left(V_{4}-V_{3}\right)=n R\left(T_{4}-T_{3}\right)$
$=2 \times R(900-1800)=-1800\, R$
$W_{\text {total }} =600\, R-1800\, R=-1200\, R$