Question

Gas fills a cylinder fitted with a frictionless piston. The initial pressure and volume are 40 MPa

and 0.05 dm3 respectively. The gas expands reversibly and polytropically to 0.5 MPa and 1 dm3

respectively. Calculate the index of expansion and the work done

Answer 1

$p_1V_1^n=p_2V_2^n,$

$\frac{p_1}{p_2}=(\frac{V_2}{V_1})^n,$

$\frac{40}{0.5}=(\frac 1{0.05})^n,$

$80=20^n,$

$n≈1.46,$

$A=\frac1{n-1}(p_1V_1-p_2V_2)=1025~J.$