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 $5\text{J}$, the work done by the gas in the process $C\to A$ is

• A. $-5\text{J}$
• B. $-10\text{J}$
• C. $-15\text{J}$
• D. $-20\text{J}$

Answer 1

The correct option is A $-5\text{J}$

$\Delta W_{AB}=P\Delta V=\left(10\right)(2-1)=10\text{J}$
$\Delta W_{BC}=0$ (as $V=\text{constant}$)
From first law of thermodynamics
$\Delta Q=\Delta W+\Delta U$
$\Delta U=0$ (process $ABCA$ is cyclic)
$\therefore \Delta Q=\Delta W_{AB}+\Delta W_{BC}+\Delta W_{CA}$
$\Delta W_{CA}=\Delta Q-\Delta W_{AB}-\Delta W_{BC}=(5-10-0)\text{J}$
$=-5\text{J}$