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

`1200kPa ; -480J`

Explanation

Here, `gamma=1.5, V_(1)=1600c.c., V_(2)= 400c.c`,
`P_(1)= 150kPa, P_(2)=?, W=?`
In an adiabatic process, `P_(2)V_(2)^(gamma)=P_(1)V_(1)^(gamma)`,
`P_(2)=P_(1)((V_(1))/(V_(2)))^(gamma)= 150 ((1600)/(400))^(1.5)=1200kPa`
`W=(R(T_(1)-T_(2)))/((gamma-1))=(P_(1)V_(1)-P_(2)V_(2))/(gamma-1)`
`=(150xx10^(3)xx1600xx10^(6)-1200xx10^(3)xx400xx10^(-6))/(1.5-1)`
`(240-480)/(0.5)= -480J`