Question

A gas is confined to a subvolume v₁ in an insulated rigid container. the container has an adjoining subvolume v₂ initially evacuated which can be connected to v₁ by opening the valve. if the valve is opened and the gas flows out of v₁finally filling the entire volume v₁+v₂, calculate the work done by the gas in this expansion and change the internal energy of the gas

Answer 1

Let the final temperature be T and n1​ & n2​ be the no. of moles of gas in each container
Using conservation of energy
(n1​+2​)CV​T=n1​CV​T1​+n2​CV​T2​
⇒(RT1​
P1​V1​​+RT2​
P2​V2​​)T=R
P1​V1​​+R
P2​V2​​
⇒(T1​T2​
P1​V1​T2​+P2​V2​T1​​)T=P1​V1​+P2​V2​
⇒T=P1​V1​T2​+P2​V2​T1​
T1​T2​(P1​V1​+P2​V2​)​