Question

In the adjoining graph, possible paths $ABC$ and $AC$ for changing a gas from the thermodynamic state $A$ to the state $C$: (i) Along which path greater amount of work will have to be done? (ii) If the internal energy of the gas at the state $A$ be $5$ joule, and $100$ then calculate the internal energy of the gas at the state $C$.

Answer 1

Work done is area under curve
(a) $BC$ work done $=40\times (4-1)=120J$
(b) $AC$ work done $=\frac{1}{2}\times (10+40)\times 3=75J$
$U_A=5J$
$Q=\Delta U_{AC}+W_{AC}$
$100J=\Delta U_{AC}+75$
$U_{AC}=25$
$U_C-U_A=25$
$U_C=30J$
Work done max along $BC=120J$