The ratio of the molar specific heat capacity at constant pressure to that at constant volume,g,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

For an adiabatic process, the relation between pressure and volume is given by $P_1V_1^\gamma = P_2V_2^\gamma$, where $\gamma$ is the ratio of specific heats ($C_p/C_v$), $P_1$ and $P_2$ are the initial and final pressures, and $V_1$ and $V_2$ are the initial and final volumes, respectively. Given $\gamma = 7/5$, $V_1 = 0.30$ m³, $V_2 = 0.10$ m³, and $P_1 = 1.0 \times 10^5$ Pa (atmospheric pressure), we can solve for $P_2$. Rearranging the equation for $P_2$, we get $P_2 = P_1 \times (V_1/V_2)^\gamma$. Substituting the given values, $P_2 = 1.0 \times 10^5 \times (0.30/0.10)^{7/5}$, which calculates to approximately $4.7 \times 10^5$ Pa, making option E the correct answer.

The Ratio of the Molar Specific Heat Capacity at Constant