A gas is heated in such a way that its pressure and volume both become double. Now by decreasing temperature, some of air molecules were introduced into the container to maintain the increased volume and pressure. Assuming `1//4^(th)` of the initial number of moles has been given for this purpose. By what fraction of temperature has been raised finally of initial absolute temperature.

Explanation

Initially, `P_(1)=P,V_(1)=V`,
Then after heating, `P_(2)=2P, V_(2)=2V`
`(P_(1)V_(1))/(T_(1))=(P_(2)V_(2))/(T_(2)) :. (PV)/(T_(1))=(2Pxx2V)/(T_(2)) " or " T_(2)=4T_(1)`
New P and V are kept constant (double values) when air is taken in. If initialy, npo of moles of air `(n_(1))=n`
Then now no. of moles `=n+(n)/(5)=(5)/(4)n`
Now temperature is raised from 4 `T_(1)` to `T_(f)` (final temperature)
Applying PV=nRT
As P and V are kept constant, `n_(i)T_(i)=n_(f)T_(f)`
`:. " "nxx4T_(1)=(5)/(4)nxxT_(f)" or " T_(f)=(16)/(5)T_(1)`