Question

The amount of work done by a gas which is being isobarically heated from $27^{\circ} C$ to $127^{\circ} C$ in a vessel closed by a movable piston with a cross-sectional area of $20\, cm ^{2}$ and weighing $5\, kg$ in the following two cases is: $(1) w_{1}$, when the vessel is arranged horizontally (Figure $a$), and $(2)$ $w_{2}$, when the vessel is arranged vertically (Figure $b$). If the initial volume of the gas is $6$ litres, then find $\left(w_{1}+w_{2}\right)$ in joule. Assume standard atmospheric pressure $=100\, kPa$ and neglect friction.

Answer 1

$ P V =n R T $
$ P V =n R \times 300 $
$ P V^{\prime} =n R \times 400 $
$ \frac{V^{\prime}}{V} =\frac{4}{3} $
$ V^{\prime} =8 \text { litres }$
$ w_{1} =P_{0} \Delta V$
$=10^{5} \times[8-6] \times 10^{-3}=200\, J $
$ P_{2} =P_{0}+\frac{m g}{A}=10^{5}+\frac{5 \times 10}{20 \times 10^{-4}}$
$=10^{5}+2.5 \times 10^{4} $
$ w_{2} =12.5 \times 10^{4} \times[8-6] \times 10^{-3}=250 \,J $
$w_{1} +w_{2}=450 \,J$