Question
An ideal gas is taken through the cycle $$A \to B \to C \to A,$$ as shown in the figure. If the net heat supplied to the gas in the cycle is $$5\,J,$$ the work done by the gas in the process $$C → A$$ is
An ideal gas is taken through the cycle $$A \to B \to C \to A,$$ as shown in the figure. If the net heat supplied to the gas in the cycle is $$5\,J,$$ the work done by the gas in the process $$C → A$$ is
A.
$$ - 5 \,J$$
B.
$$ - 10\, J$$
C.
$$ - 15\, J$$
D.
$$ - 20\, J$$
Answer :
$$ - 5 \,J$$
Solution :
For cyclic process ;
$$\eqalign{ & {Q_{{\text{cyclic}}}} = {W_{AB}} + {W_{BC}} + {W_{CA}} \cr & = 10\,J + 0 + {W_{CA}} \cr & = 5\,J \cr & \Rightarrow \,\,{W_{CA}} = - 5\,J \cr} $$
For cyclic process ;
$$\eqalign{ & {Q_{{\text{cyclic}}}} = {W_{AB}} + {W_{BC}} + {W_{CA}} \cr & = 10\,J + 0 + {W_{CA}} \cr & = 5\,J \cr & \Rightarrow \,\,{W_{CA}} = - 5\,J \cr} $$
