Molar heat capacities: An ideal gas with γ = 1.67 is initially at 0°C in a volume of 10.0 L at a pressure of 1.00 atm. It is then expanded adiabatically to a volume of 10.4 L. What is the final temperature of the gas?

Question

Quizplus · Accepted Answer

For an adiabatic process, the final temperature can be calculated using the formula $T_f = T_i \left(\frac{V_i}{V_f}\right)^{\gamma-1}$, where $T_i$ and $T_f$ are the initial and final temperatures in Kelvin, $V_i$ and $V_f$ are the initial and final volumes, and $\gamma$ is the heat capacity ratio. Given $\gamma = 1.67$, $T_i = 273 K$ (0°C), $V_i = 10.0 L$, and $V_f = 10.4 L$, we can calculate $T_f$. Converting the final temperature back to Celsius gives a result close to -7.1°C, indicating an adiabatic cooling effect due to the expansion.

Molar Heat Capacities: an Ideal Gas with γ = 1