Internal energy of n ₁ moles of hydrogen at temperature T is equal to internal energy of m ₂ moles of helium at temperature 2T. The ratio n₁ n₂ is

Step-by-step solution

The internal energy U of an ideal gas is given by U = n C_V T , where n is the number of moles, C_V is the molar heat capacity at constant volume, and T is the temperature. For hydrogen ( H₂ ), which is a diatomic gas, the degrees of freedom f = 5 . Thus, C_ V, H₂ = f 2 R = 5 2 R . The internal energy is U₁ = n₁ 5 2 R T . For helium ( He ), which is a monatomic gas, the degrees of freedom f = 3 . Thus, C_ V, He = f 2 R = 3 2 R . The internal energy is U₂ = n₂ 3 2 R (2T) . Equating the internal energies U₁ = U₂ : n₁