Consider a monatomic ideal gas that undergoes an adiabatic expansion such that its volume doubles. The ratio of the final temperature over the initial temperature is

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For a monatomic ideal gas undergoing adiabatic expansion, the relationship between the final temperature (Tf) and the initial temperature (Ti) can be described using the equation $T_iV_i^{\gamma-1} = T_fV_f^{\gamma-1}$, where $\gamma$ (gamma) is the heat capacity ratio (Cp/Cv). For a monatomic ideal gas, $\gamma = 5/3$. Given that the volume doubles ($V_f = 2V_i$), we can substitute into the equation to find the ratio $T_f/T_i$. Rearranging the equation gives us $T_f/T_i = (V_i/V_f)^{\gamma-1}$. Substituting $V_f = 2V_i$ and $\gamma = 5/3$, we get $T_f/T_i = (1/2)^{2/3}$, which approximately equals 0.63.

Consider a Monatomic Ideal Gas That Undergoes an Adiabatic Expansion