Question

The figure shows two paths through which a gas can be taken from state $A$ to state $B$. If the ratio of work done by the gas in the two paths is $x / y$, then find $(x+y)$.

Answer 1

$\Delta W_{A B}=$ Area under $A \rightarrow B$ bounded by volume axis.
$=10 \times 10^{3}(25-10) \times 10^{-6} +\frac{1}{2}(25-10) \times 10^{-6} \times 20 \times 10^{3}$
$=0.15+0.15=0.3 \,J $
In path $ A \rightarrow C \rightarrow B$,
$\Delta W_{A C B}=30 \times 10^{3}(25-10) \times 10^{-6}$
$=0.45 \,J$