The volume of a gas is reduced adibatically to `(1//4)` of its volume at `27^(@)C` if `y = 1.4` The new temperature will be

Options

A. `300 xx (4)^(0.4) K`
B. `150 xx (4)^(0.4) K`
C. `250 xx (4)^(0.4) K`
D. None of these

Answer

a

Explanation

For adiabatic change the relation between temperature and volume is
`TV^(gamma-1) = "constant"`
where `gamma` is ratio of specific heats of the gas
Given `T _(1) = 27 + 273 = 300 K , V_(1)= V, V_(2) = (V)/(4)`
`T_(1)V_(1)^(gamma- 1) = T_(2) V_(2)^(gamma - 1)`
`rArr T_(2) = ((V_(1))/(V_(2)))^( gamma - 1) xx T_(1)`
`T_(2)= ((V)/(V//4))^(1.4 - 1) xx 300`
`T_(2) = (4)^(0.4) xx 300 xx (4)^(0.4) K`.