Four moles of oxygen being initially at temperature `T_0=300K` is adiabatically compressed so the pressure becomes `128P_0`,`P_0` is initial pressure find
(a) the gas temperature after compression
(b) The work that has been performed on the gas.

Explanation

`n=4`,`T_1=T_0=300K`,`P_1=P_0`,`P_2=128P_0`
`gamma=1.4=(7)/(5)`
(a) For adiabatic process
`(T^(gamma))/(P^(gamma-1))=`constant
`(T_1^(gamma))/(P_1^(gamma-1))=(T_2^(gamma))/(P_2^(gamma-1))`
`T_2=T_1((P_2)/(P_1))^((gamma-1)/(gamma))=300((128P_0)/(P_0))^(((7)/(5)-1)/((7)/(5)))`
`=300(128)^((2)/(7))=300[(2)^7]^((2)/(7))`
`=300xx2^2=1200K`
(b) `DeltaW_(adi)=(nR(T_1-T_2))/(gamma-1)`
`=(4xx8.3(300-1200))/(1.4-1)`
`=-83xx500`
`=-74700J`