Air open vessel at `127^(@)C` is heated until `1//5^(th)` of air in it has been expelled. Assuming that the volume of vessel remains constant the temperature to which the vessel has been heated is

Explanation

In this problem, the volume of the vessel is constant. As the vessel is open, its pressure will also remain constant.
According to ideal gas equation, `PV = nRT`
`PV = n_(1)RT_(1)` and `PV = n_(2)RT_(2)`
or `n_(1)RT_(1) = n_(2)RT_(2)` or `(n_(1))/(n_(2)) = (T_(2))/(T_(1))`
Let the initial no. of moles `(n_(1)) = 1`
`:.` Final no. of moles `(n_(2)) = 1 - (3)/(5) = (2)/(5) = 0.4`
Initial temperature `(T_(1)) = 27+273 = 300 K`
Final temperature `(T_(2)) = ?`
Substituting the values, `T_(2) = (2) = (n_(1) xx T_(1))/(n_(2)) = (1 xx 300 K)/(0.4) = 750 K`
`:.` Final temperature `(T_(2)) = 750-273 = 477^(@)C`.