Question

An ideal monoatomic gas undergoes adiabatic free expansion from $16bar$, $2L$, $300K$ to $16L$.

• A. The final pressure of gas becomes zero
• B. The final pressure of gas becomes $2bar$
• C. The final temperature of gas becomes $300\times {\left(\frac{2}{16}\right)}^{\frac{2}{3}}K$
• D. The final temperature of gas becomes $300K$

Answer 1

Answer: (B), (D)

The correct options are
B The final pressure of gas becomes $2bar$
D The final temperature of gas becomes $300K$

In adiabatic free expansion $q=0$ and $W=0$.
According to first law of thermodynamics,
$\Delta U=q+W$
$\therefore \Delta U=0$
Hence the process is also isothermal and thus the initial and final temperature are same.

So the final temperature of the gas is $300K$

Since the process is isothermal,
$P_1{V}_1=P_2{V}_2$
$\Rightarrow 16\times 2=16\times P_2$
$P_2=2bar$