Answer to Question #116903 in Mechanical Engineering for alex

Question #116903
Air initially at 75 psia and 65 0F is compressed to a final pressure of 300 psia and temperature of 320 0F. Find the polytropic exponent for the process
1
Expert's answer
2020-05-19T09:13:05-0400

Equation of polytropic process in terms of pressure and temperature is "p^{1-n}T^{n} = const".

Writing this explicitly for initial and final state, obtain "p_1^{1-n} T_1^{n} = p_2^{1-n}T_2^n", from where "\\left( \\frac{p_1}{p_2} \\right) ^{1-n} = \\left( \\frac{T_2}{T_1} \\right)^n", or "\\frac{p_1}{p_2} = \\left( \\frac{p_1 T_2}{p_2 T_1} \\right)^n". Using last equation, "n = log_{\\left( \\frac{p_1 T_2}{p_2 T_1} \\right)}\\frac{p_1}{p_2} \\approx -6.7".


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