Question

Consider the cyclic process $ABCD$, shown in the figure, performed on a sample of $2.0\text{mole}$ of an ideal gas. A total of $1200J$ of heat is withdrawn from the sample in the process. Find the magnitude of the work done (𝑖𝑛 𝑗𝑜𝑢𝑙𝑒𝑠) by the gas during the part $BC$. $(R=8.3J/K)$

• A.
  $3625J$
• B.
  $1550J$
• C.
  $2580J$
• D.
  $4520J$

Answer 1

The correct option is D

$4520J$
Formula used: $W=nR\Delta T$
Work done by the gas during $AB$ part,
$W_{AB}=nR\Delta T=400R$
Part 𝐶𝐴 is isochoric process, hence work done in it will be zero,
$W_{CA}=0$
Formula used:$Q=\Delta U+W$
Given, heat withdrawn from the sample,
$Q=1200J$
For the cyclic process $A,B,C,A$
$\Delta U=0$
$Q=W_{AB}+W_{BC}+W_{CA}$
$\Rightarrow -1200J=W_{AB}+W_{BC}+W_{CA}$
$(-ve$ sign as heat is withdrawn from the sample)
$\Rightarrow W_{BC}=-1200-400R$
$\Rightarrow W_{BC}=-1200-3320=-4520J$