Question

At the beginning of compression a cylinder contains 800 cm3 of gas at a pressure of 130kN/m2 absolute. Compression takes place according to the law PVn = constant until the pressure is 750kN/m2. If the final volume is 1/5 of the initial volume, determine the value of polytropic process index n.

Answer 1

$p_1V_1^n=p_2(0.2V_1)^n\to p_1=p_2(0.2)^n$

$\frac{p_1}{p_2}=0.2^n\to \ln{\frac{p_1}{p_2}}=n\ln{0.2}$

$n=\ln{\frac{p_1}{p_2}}/\ln{0.2}=\ln{\frac{130}{750}}/\ln{0.2}=1.09$. Answer