A gas is suddenly compressed to `1/4th` of its original volume. Caculate the rise in temperature when original temperature is `27^(@)C. gamma= 1.5`.

Options

A. `300^(@)C`
B. `327^(@)C`
C. `327K`
D. `600K`

Answer

A

Explanation

Here `V_(2)= 1/4V_(1), T_(1)= 27^(@)C= 27+273=300K`
`gamma= 1.5, T_(2)-T_(1)=?`
As the change is adiabatic, therefore,
`T_(2)V_(2)^(gamma-1)= T_(1)V_(1)^(gamma-1)`
`T_(2)=T_(1)(V_(1)/(V_(2)))^(gamma-1)`
`=300(4)^(1.5-1)= 300xx600K`
`:.` Rise in temp. `= T_(2)-T_(1)`
`=600-300= 300K or 300^(@)C`