Some amount of air, initially at STP, is adiabatically compressed to `1/5 th` its initial volume. Determine the rise in temperature. Given, `gamma = 1.41`.

Explanation

In an adiabatic process, `TV^(gamma - 1) = "constant"`
or, `T_(1)V_(1)^(gamma - 1) = T_(2)V_(2)^(gamma - 1)`
or, `T_(2) = T_(1) ((V_1)/(V_2))^(gamma - 1)`
Here, `T_(1) = 0^(@)C = 273 K , (V_1)/(V_2) = 5, gamma - 1 = 1.41 - 1 = 0.41`
`:. T_(2) = 273 xx (5)^(0.41)`
`= 528.13 K = (528.13 - 273)^(@)C = 255.13^(@)C`
`:.` Rise in temperature = `255.13 - 0 = 255.13^(@)C`.