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JEE MainPhysicsKinetic Theory of Gases

Equal masses of helium gas and nitrogen gas are confined in a single rigid container at a constant temperature. The ratio of the total internal energy of the helium gas to that of the nitrogen gas is:

Options

  1. A3:5
  2. B21:5
  3. C7:1
  4. D5:21

Correct answer

B. 21:5

Step-by-step solution

The total internal energy U of an ideal gas sample is given by U = f 2 nRT , where f is the degrees of freedom and n is the number of moles. Let the mass of each gas be m . For helium (a monoatomic gas), f_ He = 3 and its molar mass is 4 g/mol . Number of moles of helium, n_ He = m 4 . Total internal energy of helium, U_ He = 3 2 ( m 4 ) RT . For nitrogen (a diatomic gas), f_ N ₂ = 5 and its molar mass is 28 g/mol . Number of moles of nitrogen, n_ N ₂ = m 28 . Total internal energy of nitrogen, U_ N ₂ = 5 2 ( m 28

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