A quantity of an ideal gas at `17^(@)C` is compressed adiabatically to `1/8th of its initial volume. Calculate the final temp. if the gas in monoatomic.

Explanation

Here, `T_(1)= 17^(@)C= 17+273= 290K`
`V_(2)= 1/8V_(1), T_(2)=?`
For monoatomic gas `gamma = 5//3`
As the process 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)`
`= 290(8)^(5//3-1)=(290)xx(8)^(2//3)`
`= 290xx4= 1160K`