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.
1
Expert's answer
2020-08-20T09:48:54-0400

Find the final pressure:


"p_1V_1^3=p_2V_2^3,\\\\\\space\\\\\np_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\\\\\nW=\\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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