An ideal monoatomic gas at `27^(@)C` is compressed adiabatically to `(8)/(27)` times of its present volume. The increase in temperature of the gas is

Options

A. `375^(@)C`
B. `402^(@)C`
C. `175^(@)C`
D. `475^(@)C`

Answer

B

Explanation

`V_(1)=v,V_(2)=(8)/(27),gamma=5/3`
`T_(1)=27+273=300K`
`therefore (V_(1))/(V_(2))=(27)/(8)`
`T_(1)V_(1)^(gamma-1)=T_(2)V_(2)^(gamma-1)and (T_(2))/(T_(1))=((V_(1))/(V_(2)))^(gamma-1)`
`T_(2)=((27)/(8))^(5//3-1)xxT_(1)=((27)/(8))^(2//3)xxT_(1)`
`=((3)/(2))^(2)xx300=675K`
`therefore t_(2)=675-273=402^(@)C`