Q. An ideal gas is expanded adiabatically at an initial temperature of $300\ K$ so that its volume is doubled. The final temperature of the hydrogen gas is $(\gamma = 1.40)$

A) $227.36\ K$
B) $500.30\ K$
C) $454.76\ K$
D) $- 47℃$
Explanation

(a) $TV^{\gamma - 1} =$ constant $\Rightarrow \frac{T_{2}}{T_{1}} = \left( \frac{V_{1}}{V_{2}} \right)^{\gamma - 1}$
$\Rightarrow T_{2} = T_{1}\left( \frac{V_{1}}{V_{2}} \right)^{\gamma - 1}$
$\Rightarrow T_{2} = 300\left( \frac{1}{2} \right)^{0.4} = 227.36\ K$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.

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