Question

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 if the gas is compressed to `200 cm^(3) (a) in a short time (b) in a long time . Take gamma= 1.4.

Answer 1

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)`
`=(300K)xx[(800)/(200)]^(0.4) = 522K`
Rise in temperature = `T_(2) -T_(1) = 222 K`
(b) When the gas is compressed in a long time. the process is isothermal thus, the temperature remains equal to the temperature of the sourrounding that is `27^(@)C`. THe rise in temperature = 0.