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?
A) -7.1°C
B) 2.5°C
C) -23°C
D) 68°C
E) -20°C

Question

Quizplus · Accepted Answer

For an adiabatic process, the final temperature can be calculated using the formula $T_2 = T_1 \left(\frac{V_1}{V_2}\right)^{\gamma-1}$, where $T_1$ and $T_2$ are the initial and final temperatures in Kelvin, $V_1$ and $V_2$ are the initial and final volumes, and $\gamma$ is the heat capacity ratio. Converting the initial temperature to Kelvin, $T_1 = 273 K$, and using the given volumes and $\gamma = 1.67$, we can solve for $T_2$. The calculation shows a decrease in temperature, which, when converted back to Celsius, gives a value close to -7.1°C, indicating an adiabatic expansion that cools the gas.

An Ideal Gas with γ = 1