An ideal gas is allowed to expand adiabatically until its volume increases by 50%.By approximately what factor is the pressure reduced? ($\gamma$ = 5/3. )
A)1.5
B)2.0
C)2.5
D)3.0
E)3.5

Question

Quizplus · Accepted Answer

In an adiabatic process for an ideal gas, $ P V^\gamma = \text{constant} $. Given $\gamma = \frac{5}{3}$, if the volume increases by 50%, the new volume is $1.5V$. Therefore, the pressure is reduced by a factor of $ (1.5)^{-\frac{5}{3}} \approx 0.5 $, meaning the pressure is halved, or reduced by a factor of 2.

An Ideal Gas Is Allowed to Expand Adiabatically Until Its γ\gammaγ

An Ideal Gas Is Allowed to Expand Adiabatically Until Its $\gamma$