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?

Explanation

Here, `gamma= 1.5, V_(1)= 1600 c.c., V_(2)= 400 c.c.`,
`P_(1)= 150 k Pa= 150xx10^(3)Pa, P_(2)=?`
In an adiabatic process, `P_(2)V_(2)^(gamma)= P_(1)V_(1)^(gamma)`
`:. P_(2)= P_(1)(V_(1)^(gamma)/V_(2))=150((1600)/(400))^(1.5)= 1200 K Pa`
Work done on the gas in the process
`W=(P_(1)V_(1)-P_(2)V_(2))/(gamma-1)=((150xx10^(3))(1600xx10^(-6))-(1200xx10^(3))(400xx10^(-6)))/(1.5-1)=(240-480)/(0.5)= -480J`