n1 moles of N2 at temp T have same internal energy as n2 moles of He at temp 2T find n1/n2

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Arun · Answer

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.∆T For 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 He U₁ = U₂ 5n₁RT/2 = 3n₂RT 5n₁ = 6n₂ n₁/n₂ = 6/5 , hence ratio of n₁ and n₂ is 6 : 5

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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

n1 moles of N2 at temp T have same internal energy as n2 moles of He at temp 2T find n1/n2

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