Answer to Question #292166 in Physics for Biola

Question

The air in cyclinder is compressed to of its initial volume, if initial pressure is 1×10^5 Pascal and initial temperature is 27°C. Find the final pressure and temperature often compression. Take gamma= 1.4

Answer 1

Assuming the gas was compressed to n/m of its initial volume.

Apply the combined gas law:

$P_1V_1^\gamma=P_2V_2^\gamma,\\\space\\ P_2=P_1\bigg(\dfrac{V_1}{V_2}\bigg)^\gamma=P_1\bigg(\dfrac mn\bigg)^\gamma,\\\space\\ P_2=1·10^5(m/n)^{1.4}.$

The temperature:

$P_1^{1-\gamma}T_1^\gamma=P_2^{1-\gamma}T_2^\gamma,\\\space\\ T_2=T_1{(P_1/P_2)^{\frac1\gamma-1}}=300[(n/m)^{1.4}]^{-2/7}.$