Question

$1litre$ of an ideal gas $(\gamma =1.5)$ at $300K$ is suddenly compressed to half its original volume.
What is the final temperature?

• A. $44K$.
• B. $24K$.
• C. $524K$.
• D. $424K$.

Answer 1

The correct option is D $424K$.

Given : 1 litre1 litre of an ideal gas (γ=1.5)(γ=1.5) at 300 K300 K is suddenly compressed to half its original volume.

What is the final temperature?

Solution :

$\gamma =1.5$ , T=300K , V=1L , V=1/2 L

The process is adiabatic as it is sudden

$T_1{V}_1^{\gamma -1}$=$T_2{V}_2^{\gamma -1}$

$300K(1{)}^{1.5-1}$=$T_2(\frac{1}{2}{)}^{1.5-1}$

On solving we get $T_2=300\sqrt{2}$ = 424.2 $\approx$ 424

The Correct Opt =D