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.

Options

A. `(4)/(5)` times
B. `(16)/(7)` times
C. `(16)/(5)` times
D. `(8)/(5)` times

Answer

C

Explanation

`{:((P_(1)V_(1))/(T_(1)) = (2P_(1) xx 2V_(1))/(T_(2)),4T_(1) xx n_(1) =T_(2)'n'_(2),),(T_(2) = 4T_(1),4T_(1)n_(1) = T_(2)^(') xx (5)/(4)n_(1) (n_(2) = n_(1) + (n_(1))/(4)),),(,"Therefore" T_(2)^(') = (16)/(5)T_(1),):}`