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Two closed vessels of equal volune conta...

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?

Text Solution

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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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