Two closed vessels of equal volune contain air at 105kPa, 300K and are connected through a narrow tube. If one of the vessels is mow maintained at 300K and the other at 400K, what will be the pressure in the vessels?

Explanation

Let the initial pressure, volume and temperature in each vessel be `p_(0)(=105 kPa), V_(0) and T_(0)(=300K)`. Let the number of molesin each vessel be n. When the first vessel is maintained at temperature `T_(0)` and the other is maintained at `T'=400K`, the pressuress change, Let the common pressure become p' and the number of moles in the two wessels become `n_(1)` and `n_(2)`. We have
`p_(0)V_(0)=nRT_(0) ` ...(i)
`p'V_(0)=n_(1)RT_(0)` ...(ii)
`p'V_(0)=n_(2)RT' ...(iii)
and `n_(1)+n_(2) =2_(n). ...(iv)`
Putting `n, n_(1) and n_(2)` from (i),(ii) and (iii) in (iv),
`(p'V_(0))/(RT_(0))+(p'V_(0))/(RT')=2(p_(0)V_(0))/(RT_(0))`
or, `p'((T'+T_(0))/(T_(0)T'))=(2p_(0))/(T_(0)
or, p'=(2p_(0)T')/(T'+T_(0))`
`=(2xx105kPaxx400K)/(400K+300K)=120kPa`.
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