If the pressure of a gas contined in closed vessel in increased by `0.4%` when heated by `1 K`, its initial temperature must be:

Options

A. `250^(@)C`
B. `100^(@)C`
C. `-75^(@)C`
D. `-23^(@)C`

Explanation

Let `T_(1) =T` and `P_(1) =P`
`T_(2) = (T+1)` and
`P_(2) = P + (0.4P)/(100) = (100.4)/(100) P`
using `(P_(1)P_(1))/(T_(1)) = (P_(2)V_(2))/(T_(2))`
`(PV)/(T) = (100.4PxxV)/(100xx(T+1))`
`T =250K = -23^(@)C` .