Question

2) (5 pt) A gas in a piston cylinder devic volume are related as follows P-A V2, where A is a constant. Write the expression f boundary work done by the system in terms of initial and final volumes of the gas e undergoes a compression where pressure and traneitions from a compressed

Answer 1

Boundary Work done by the system

$W=\int_{V_{i}}^{V_{f}}PdV$

$W=\int_{V_{i}}^{V_{f}}AV^{2}dV=A\int_{V_{i}}^{V_{f}}V^{2}dV$

$W=A\left [ \frac{V^{3}}{3} \right ]_{V_{i}}^{V_{f}}$

$W=\frac{1}{3}A(V_{f}^{3}-V_{i}^{3})$