Two closed vessels of equal volume contain air at `P_(0)` pressure, `T_(0)` temperature and are connected through a narrow tube, If one of the vessels is now maintained at `T_(0)` and other at T, what will be the pressure in the vessels?

Explanation

Lets say volume of each vessel be `V_(0)`
lets say initially n moles where present in each vessel
`n=(P_(0)V_(0))/(RT_(0))`

thus total no. pf moles in the system `=(2P_0V_0)/(RT_0)`
Finally lates say `n_(L)` moles where present in left vessel and `n_(r)` moles where present in right vessel.
`n_(L)=(PV_0)/(RT_0)" " &" " n_(R)=(PV_0)/(RT_0)`
here P is the pressure in vessel
`n_(L)+n_(R)=2n` (no. of moles is constant)
`(PV_0)/(RT)+(PV_0)/(RT_0)=(2P_(0)V_(0))/(RT_(0))`
`P=(2p_(0))/(T_(0)(1/T+1/(T_(0)))`