Air is filled at `60^(@)C` in a vessel of open mouth. The vessle is heated to a temperature `T` so that `1//4th` of air escapes. Assuming the volume of vessel remaining constant, the value of `T` is

Options

A. `80^(@)C`
B. `440^(@)C`
C. `333^(@)C`
D. `171^(@)C`

Answer

D

Explanation

d. `M_(1) = M, T_(1) = 60 + 273 = 333 K`
`M_(2) = M - (M)/(4) = (3 M)/(4)` (as `1//4th` part of air escapes)
If pressure and volume of the gas remain constant, then `MT=` constant
`:. (T_(2))/(T_(1)) = (M_(1))/(M_(2)) = ((M)/(3M//4)) = (4)/(3)`
`implies T_(2) = (4)/(3) xx T_(1) = (4)/(3) xx 333 = 444 K = 171^(@)C`