JEE Advanced2015PhysicsKinetic Theory of GasesActual
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)
Options
- AThe average energy per mole of the gas mixture is 2 R T
- BThe ratio of speed of sound in the gas mixture to that in helium gas is 6 5
- CThe ratio of the rms speed of helium atoms to that of hydrogen molecules is 1 2
- DThe ratio of the rms speed of helium atoms to that of hydrogen molecules is 1 2
Correct answer
A. The average energy per mole of the gas mixture is 2 R T
Step-by-step solution
C V m i x = 1 3 2 R + 1 5 2 R 2 = 2 R C P m i x = 3 R γ m i x = 3 2 ⇒ f = 4 Average energy/mole = f 1 2 R T = 2 R T V s o u n d m i x t u r e V s o u n d H e = R T 2 5 R T 12 = 6 5 V r m H e V r m s H 2 = 3 R T 4 3 R T 2 = 1 2