A quantity of air is kept in a container having walls which are slightly conducting. The initial temperature and volume are `27^0C` (equal to the temperature of the surrounding) and `800cm^(3)` respectively. Find the rise in the temperature of the gas is compressed to `200 cm^(3)` (a) in a short time (b) in a long time . Take gamma= `1.4`.

Explanation

(a) When the gas is compressed in a short time, the process is abiabatic. Thus,
`T_(2) V _(2) ^(gamma -1) = T_(1) V_(1) ^(gamma -1)`
`or T _(2) =T_(1) ((V_(1))/(V _(2))) ^(gamma -1) =(300K )xx [(800)/(200)] ^(0.4)= 522K.`
Rise in temperature `= T_(2) -T_(1) =222K`
(b) (b) When the gas is compressed in a long time, the process is isothermal. Thus, the temperature remains equal to the temperature of the surrounding that is `27^(@)C.` The rise in temperature =0.