Question

A sample of gas `(gamma = 1.5)` is taken through an adiabatic process in which the volume is compressed from `1600 cm^(3)` to `400 cm^(3)`. If the initial pressure is `150 kPa`, (a) what is the final pressure and (b) how much work is done by the gas in the process?

Answer 1

`gamma=1.5=(3)/(2)`,`V_1=1600cc`,`V_2=4400cc`
`P_1=150kPa`
(a) For adiabatic process
`P_1V_1^(gamma)=P_2V_2^(gamma)`
`P_2=P_1((V_1)/(V_2))^(gamma)=(150)((1600)/(400))^((3)/(2))`
`=150xx(4)^((3)/(2))=150xx8=1200kPa`
(b) `DeltaW_(adi)=(P_1V_1-P_2V_2)/(gamma-1)`
`((150xx1600-1200xx400)xx10^3xx10^-6)/((1.5-1))`
`=-480J`