The pressure of a gas filled in a closed vessel increase by 0.4% when temperature is increased by `1^(@) C`. Find the initial temperature of the gas.

Options

A. `250 K`
B. `250^(@)C`
C. `2500 K`
D. `25^(@)C`

Answer

A

Explanation

a. `P_(1) = P, T_(1) - T, P_(2) = P + (0.4% of P)`
`implies P_(2) = P + (0.4)/(100) P = P + (P)/(250)` and `T_(2) = T + 1`
From Gay-Lussac's law
`(P_(1))/(P_(2)) = (T_(1))/(T_(2))`
`implies (P)/(P + (P)/(250)) = (T)/(T + 1)`
(as `V = ` constant for closed vessel )
By solving, we let `T = 250 K`