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JEE Main levelSingle correct optionDifficulty 2 of 3td061

A monoatomic ideal gas at $300 K$ is compressed reversibly and adiabatically to one-eighth of its original volume. The final temperature is

A $1200 K$
B $600 K$
C $900 K$
D $2400 K$

Answer: A

For a monoatomic gas

γ = 5/3

, and

T V^{γ - 1} = constant

. So

T_{2} = T_{1} (V_{1} / V_{2})^{2/3} = 300 \times 8^{2/3} = 300 \times 4 = 1200 K

.

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