Answer to Question #128831 in Mechanics | Relativity for Ariyo Emmanuel

Question #128831
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.
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Expert's answer
2020-08-20T09:48:54-0400

Find the final pressure:


p1V13=p2V23, p2=p1(V1V2)3.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=p1V1p2V22=p1V1p1V13/V222. W=101050.05101050.0530.0622=7640 J.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}.


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