Question

A fluid at 10 bar is enclosed in a cylinder behind a piston, the initial volume being 0.05 m .Calculate the work done by the fluid when it expands reversibly according to a law pv3= C to a final volume of 0.06 m3.

Answer 1

Find the final pressure:

$$p_1V_1^3=p_2V_2^3,\\\space\\ p_2=p_1\bigg(\frac{V_1}{V_2}\bigg)^3.$$

The work done by the fluid when it expands reversibly according to the law is

$$W=\frac{p_1V_1-p_2V_2}{2}=\frac{p_1V_1-p_1V_1^3/V_2^2}{2}.\\\space\\ W=\frac{10\cdot10^5\cdot0.05-10\cdot10^5\cdot\frac{0.05^3}{0.06^2}}{2}=7640\text{ J}.$$