The ratio of the molar specific heat capacity at constant pressure to that at constant volume, $\gamma$, for diatomic hydrogen gas is 7/5. In an adiabatic compression, the gas, originally at atmospheric pressure, is compressed from an original volume of 0.30 m³ to 0.10 m³. What is the final pressure of the gas?

Question

Quizplus · Accepted Answer

In an adiabatic process, $ P_1 V_1^\gamma = P_2 V_2^\gamma $. Given $ \gamma = 7/5 $, $ P_1 = 1.0 \times 10^5 $ Pa, $ V_1 = 0.30 $ m³, and $ V_2 = 0.10 $ m³, solve for $ P_2 $: $ P_2 = P_1 (V_1/V_2)^\gamma = 1.0 \times 10^5 \times (0.30/0.10)^{7/5} = 4.7 \times 10^5 $ Pa.

The Ratio of the Molar Specific Heat Capacity at Constant γ\gammaγ

The Ratio of the Molar Specific Heat Capacity at Constant $\gamma$