Question

An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume V₁ and contains ideal gas at p₁ and temprature T₁ . The other chamber has volume V₂ and contains ideal gas at pressure p₂ and temprature T₂ . If the partition is removed without doing any work on the gas the final equiblirium temprature of the gas in the cointainer will be . [AIEEE 2008, 04] ​

Answer 1

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Answer 2

Explanation:- As no work is done and system is thermally insulated from surrounding , it means sum of internal energy of gas in two partition is constant i.e ., U = U₁ + U₂

Assuming both gases have same degree of freedom , Then

internal energy , U= f(n₁ + n₂ )RT/2

and U₁ = fn₁RT₁ /2 , U₂ = fn₂RT₂/2

on Solving , [∵ pv = nrT]

common temprature ,

T = (p ₁ v₁ + p₂v₂ )T₁T₂ /P₁V₁T₁ + P₂V₂T ₁