A container having slightly conducting walls contains air. The initial temperature and volume are `47^(@)C` (equal to the temperature of the surrounding) and `400cm^(3)` respectively. Find the rise in the temperature if the gas is compressed to `200cm^(3)` (a) in a short time (b) in a short time (b) in a along time. Take `gamma = 1.4. [2^(0.4) = 1.3]`

Explanation

(a) When the gas is compressed in a short time, the process is adiabatic. Thus,
`T_(2)V_(2)^(gamma-1) = T_(1)V_(1)^(gamma-1)`
or `T_(2) = T_(1) ((V_(1))/(V_(2)))^(gamma-1) = (320K) xx [(400)/(200)]^(0.4) = 416 K`.
Rise in temperature `=T_(2) - T_(1) = 96K`.
(b) When the gas is compressed in a along time, the process is isothermal. thus, the temperature remains same that is `47^(@)C :.` The rise in temperature `=0`.