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JEE Advanced 2015Paper 1
Exam
JEE Advanced
Year
2015
Paper
Paper 1
Subject
Physics
Chapter
Kinetic Theory of Gases

JEE Advanced 2015 · Paper 1 · Physics · Kinetic Theory of Gases

A container of fixed volume has a mixture of one mole of hydrogen...

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

Options

  1. AThe average energy per mole of the gas mixture is 2RT2RT
  2. BThe ratio of speed of sound in the gas mixture to that in helium gas is 65\sqrt{\dfrac{6}{5}}
  3. CThe ratio of the rms speed of helium atoms to that of hydrogen molecules is 12\dfrac{1}{2}
  4. DThe ratio of the rms speed of helium atoms to that of hydrogen molecules is 12\dfrac{1}{\sqrt{2}}

Correct answer

A. The average energy per mole of the gas mixture is 2RT2RT

Step-by-step solution

CV(mix)=(1)(32R)+(1)(52R)2=2R{C}_{V\left(mix\right)} = \dfrac{\left(1\right)\left(\dfrac{3}{2}R\right) + \left(1\right)\left(\dfrac{5}{2}R\right)}{2} = 2R
CP(mix)=3R{C}_{P\left(mix\right)} = 3R
γmix=32⇒f=4{\gamma}_{mix} = \dfrac{3}{2} ⇒ f = 4
Average energy/mole =f12RT=2RT= f\dfrac{1}{2}RT = 2RT
(Vsound)mixture(Vsound)He=RT25RT12=65\dfrac{{\left({V}_{sound}\right)}_{mixture}}{{\left({V}_{sound}\right)}_{He}} = \dfrac{\sqrt{\dfrac{RT}{2}}}{\sqrt{\dfrac{5RT}{12}}} = \sqrt{\dfrac{6}{5}}
(Vrm)He(Vrms)H2=3RT43RT2=12\dfrac{{\left({V}_{rm}\right)}_{He}}{{\left({V}_{rms}\right)}_{{H}_{2}}} = \dfrac{\sqrt{\dfrac{3RT}{4}}}{\sqrt{\dfrac{3RT}{2}}} = \dfrac{1}{\sqrt{2}}
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