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

Options

A. `450 K`
B. `375 K`
C. `225 K`
D. `405 K`

Answer

B

Explanation

b. For an adiabatic process `TV^(gamma -1) = ` constant. Therefore
`(T_(1))/(T_(2)) = [(V_(2))/(V_(1))]^(gamma -1)`
` implies T_(2) = T_(1) [(V_(1))/(V_(2))]^(gamma-1)`
`= 300 [(27)/(8)]^(5//3 - 1) = 300 [(27)/(8)]^(2//3) = 675 K`
`implies Delta T = 675 - 300 = 375 K`