An ideal gas at `27^(@)C` is compressed adiabatically to `8//27` of its original volume. If `gamma = 5//3`, then the rise in temperature is

Options

A. `450^@C`
B. `375^@C`
C. `225^@C`
D. `405^@C`

Answer

B

Explanation

`T_1=27+273=300K,V_1=V,V_2=(8)/(27)V,T_2=?`
`T_1V_1^(gamma-1)=T_2V_2^(gamma-1)`
`T_2=T_1((V_1)/(V_2))^(gamma-1)=(300)((V)/((8)/(27)V))^((5)/(3)-1)=(300)((27)/(8))^((2)/(3))`
`=(300)[((3)/(2))^3]^((2)/(3))=(300)((3)/(2))^2`
`=300xx(9)/(4)=675K`
`DeltaT=T_2-T_1=675-300=375K=375^@C`