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 adiabetic. Thus
`T_2V_2^(gamma-1)=T_1V_1^(gamma-1)`
`T_2=T_1((V_1)/(V_2))^(gamma-1)=(300)((800)/(200))^(1.5-1)=(300)(4)^(0.5)`
`=600K`
Rise in temperature
`DeltaT=T_2-T_1=600-200=400K`
(b) When the gas is compressed in a long time, the process is isothermal.
`trangleT=0`