A monatomic ideal gas expands adiabatically from an initial volume of 72 L and an initial temperature of 350 K until its temperature falls to 290 K. What is the final volume of the gas?
A) 95 L
B) 98 L
C) 101 L
D) 104 L
E) 142 L

Question

Quizplus · Accepted Answer

For an adiabatic process, PVγ = constant, where γ is the ratio of specific heats. For a monatomic ideal gas, γ = 5/3. Thus, P1V1^(5/3) = P2V2^(5/3). Since the pressure is not given, we can write V2 = V1(T1/T2)^(3/5). Plugging in the given values, we get V2 = 72 L * (350 K / 290 K)^(3/5) = 98 L.

A Monatomic Ideal Gas Expands Adiabatically from an Initial Volume