Molar heat capacities: An adiabatic compression is performed on an ideal gas. The final pressure is equal to 0.560 times the initial pressure and the final volume equals 1.50 times the initial volume. What is the adiabatic constant for the gas?

Question

Quizplus · Accepted Answer

For an adiabatic process involving an ideal gas, the relationship between pressure (P), volume (V), and the adiabatic constant (γ) is given by $P_1V_1^\gamma = P_2V_2^\gamma$. Given $P_2 = 0.560P_1$ and $V_2 = 1.50V_1$, we can substitute these into the adiabatic equation to find γ. Rearranging the equation gives us $\gamma = \log(P_1/P_2) / \log(V_2/V_1)$. Substituting the given values, we find $\gamma \approx 1.43$, which is characteristic of diatomic gases like nitrogen and oxygen at room temperature.

Molar Heat Capacities: an Adiabatic Compression Is Performed on an Ideal