15.0 liters of an ideal monatomic gas at a pressure of 100 * 10³ Pa is expanded adiabatically (no heat transfer)until the volume is tripled.If the initial temperature of the gas was 100 K,what was it final temperature after the expansion?

Question

Quizplus · Accepted Answer

For an adiabatic process involving an ideal monatomic gas, the final temperature can be calculated using the formula $T_f = T_i(V_i/V_f)^{(\gamma-1)}$, where $T_i$ and $T_f$ are the initial and final temperatures, $V_i$ and $V_f$ are the initial and final volumes, and $\gamma$ (gamma) is the heat capacity ratio, which is 5/3 for a monatomic ideal gas. Given $V_f = 3V_i$ and $T_i = 100 K$, we find $T_f = 100 \times (1/3)^{2/3} = 100 \times (1/3)^{0.666}$. Calculating this gives a value close to 48.1 K, indicating an adiabatic cooling of the gas.

150 Liters of an Ideal Monatomic Gas at a Pressure