`300K` a gas `(gamma = 5//3)` is compressed suddenly so that its pressure becomes `1//8` of the original pressure. The final temperature of the gas is :

Options

A. `315 K`
B. `130.58 K`
C. `327^(@)C`
D. `425 K`

Answer

B

Explanation

`:' p^(1-gamma).T^(gamma)=` constant
`[P/8]^(1-gamma).T_(1)^(gamma)=` constant
`:. [1/8]^(1-gamma).[(T_(1))/T]^(gamma)=1`
or `[(T_(1))/T]^(gamma)=(8)^(1-gamma)=(8)^(1-5/3)=9^(-2//3)`
`[(T_(1))/T]^(5//3)=(8)^(-2//3)`
`:. T_(1)=Txx0.435=300xx0.435`
`=130.58 K`