Question

Internal energy of n1 moles of hydrogen at temperature t is equal to to the internal energy of n2 moles of helium at temp 2t than the ratio n1/n2 is answer

Answer 1

Hydrogen is a diatomic molecule so, molar heat capacity at constant volume of Hydrogen is 5R/2 .e.g., $C_{v_{H_2}}$ = 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., $C_{v_{He}}$ = 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

Answer 2

Answer:

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