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?
A) 7.7 L
B) 14 L
C) 22 L
D) 52 L

Question

Quizplus · Accepted Answer

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

An Ideal Gas Initially at 300 K and Occupying a Volume