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n1 moles of N2 at temp T have same internal energy as n2 moles of He at temp 2T find n1/n2
Hydrogen is a diatomic molecule so, molar heat capacity at constant volume of Hydrogen is 5R/2 .e.g., = 5R/2 , here R is universal gas constant And helium is monoatomic so, molar heat capacity at constant volume of He is 3R/2 e.g., = 3R/2 we know, internal enery , U = nCv.∆TFor Hydrogen gas ,Internal energy , U₁ = n₁ × (5R/2) × T [ as mentioned in question temperature is T for H₂ , we know Cv for H₂ = 5R/2 ]U₁ = 5Rn₁T/2 ------(1) For helium gas ,Internal energy ,U₂ = n₂ × (3R/2) × 2T [ for helium temperature is 2T and Cv is 3R/2]U₂ = 3Rn₂T ------(2) According to question,internal energy of H₂ gas = internal energy of HeU₁ = U₂5n₁RT/2 = 3n₂RT5n₁ = 6n₂n₁/n₂ = 6/5 , hence ratio of n₁ and n₂ is 6 : 5
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