First law of thermodynamics: An ideal gas initially at 300 K and occupying a volume of 20 L is adiabatically compressed. If its final temperature is 400 K and γ = 1.30, what is its final volume?

Question

Quizplus · Accepted Answer

For an adiabatic process, the relation between the initial and final temperatures (T1, T2) and volumes (V1, V2) for an ideal gas is given by $T_1V_1^{\gamma-1} = T_2V_2^{\gamma-1}$, where $\gamma$ is the heat capacity ratio. Rearranging for $V_2$, and substituting the given values ($T_1 = 300K$, $T_2 = 400K$, $V_1 = 20L$, $\gamma = 1.30$), we can solve for $V_2$, which results in approximately 7.7 L.

First Law of Thermodynamics: an Ideal Gas Initially at 300