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

Options

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

Answer

B

Explanation

For adiabatic change the relation between temperatrue and volume is
`TV^(gamma-1)` = consta nt
where `gamma` is ratio of specific heats of the gas.
Given `T_(1) = 27+273=300K, V_(1)= V , V_(2) =V/4`
`T_(1)V_(1)^(gamma-1) = T_(2)V_(2)^(gamma-1)`
`implies T_(2) = ((V_1)/(V_2))^(gamma-1) xx T_(1)`
`=((V)/(V//4))^(1.4-1)xx300`
`=(4)^(0.4)xx300=300xx(4)^(0.4)K`.