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 K
B. 375 K
C. 225 K
D. 405 K

Answer

B

Explanation

As `TV^(gamma-1)` = constant
`implies T_2=T_1((V_1)/(V_2))^(gamma-1) implies T_2 =300((27)/(8))^(5/3-1) = 300((27)/(8))^(2/3)`
`implies T_2=300(3/2)^2=300 xx 9/4 = 675 K`
Now change in temperature
`Delta T=675-300=375 K`