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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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Grade:12th pass

1 Answers

Arun
25763 Points
one year ago
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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