Question

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

Answer 1

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, $n = log_{\left( \frac{p_1 T_2}{p_2 T_1} \right)}\frac{p_1}{p_2} \approx -6.7$.