Question

An ideal gas is taken through the cycle $A\to B\to C\to A,$ as shown in figure. If the net heat supplied to the gas in the cycle is $5J$, the work done by the gas in the process. $C\to A$ is

• A. - 5 J
• B. - 10 J
• C. -15 J
• D. -20 J

Answer 1

Answer: (A)

Work done by gas is given by
$W=P\Delta V$
Total work done by gas is

$W=W_{AB}+W_{BC}+W_{CA}\dots$(i)
From first law of thermodynamics
$\Delta Q=\Delta U+W\dots$(ii)
Here $W_{AB}=P\Delta V=10(2-1)=10J$
$W_{BC}=P\Delta V=2\times 0=0$
Hence, Eqs. (i) and (ii) will be written as
$5=0+\left(10+0+W_{CA}\right)$
$\Rightarrow W_{CA}=-5J$