JEE Advanced 2015 · Paper 1 · Physics Q16

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PhysicsMultiple correct+4 / -2Question 16 of 60

A container of fixed volume has a mixture of one mole of hydrogen and one mole of helium in equilibrium at temperature $T$ . Assuming the gases are ideal, the correct statement(s) is(are)

The average energy per mole of the gas mixture is

2RT

The ratio of speed of sound in the gas mixture to that in helium gas is

\sqrt{6/5}

The ratio of the rms speed of helium atoms to that of hydrogen molecules is 1/2.

The ratio of the rms speed of helium atoms to that of hydrogen molecules is

1/\sqrt2

Answer and worked solution

Official answer: A, B, D

(A) Average energy per mole: $\frac12\left(\frac52RT+\frac32RT\right)=2RT$ . True.
(B) For the mixture, $C_V=2R$ , $C_P=3R$ , $\gamma=\frac32$ and $M=3$ g/mol. For helium, $\gamma=\frac53$ and $M=4$ g/mol. So
$\frac{v_{mix}^2}{v_{He}^2}=\frac{1.5/3}{(5/3)/4}=\frac65.$
True.
(C), (D) $v_{rms}\propto M^{-1/2}$ , so $\dfrac{v_{He}}{v_{H_2}}=\sqrt{\dfrac24}=\dfrac1{\sqrt2}$ . (D) is true and (C) is false.

(A), (B), (D)

Topics:Specific heats of gases Molecular speeds Speed of waves

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JEE Advanced 2015 · Paper 1, Physics question 16