A gas at constant pressure `P_1, volume V_1` and temperture `T_1` is suddenly compressed to `V_1/2` and then slowly expanded to `V_1` again.Find the final temperature and pressure.

Answer

1246.5 J

Explanation

`(P_(1),V_(1),T_(1))` Suddenly adiabatic `(P_(1),(V_(1))/(2),T_(2))" "(P_(3),V_(1),T_(3))` Slowly Thermal equation `rArr T = constant`
`P_(2) = P_(1)((V_(1))/(V_(1))xx2)^(2) = 2^(r) P_(1)`
`(P_(2)V_(2))/(T_(2)) =(P_(1)V_(1))/(T_(1))`
`(P_(2)V_(1))/(T_(2))=(P_(1)V_(1))/(T_(1))`
`T_(2) = ((P_(2)V_(2))T_(1))/(P_(1)V_(1)) = (2^(r)P_(1).(V_(1//2))T_(1))/(P_(1)V_(1))`
`=2^(r-1)T_(1)`
`PV = Constant rArr P_(3)V_(1) =P_(1)(V_(1))/(2) rArr P_(3)=(P_(2))/(2) =(2^(r)P_(1))/(2) =2^(r-1) P_(1)`
`T_(3) =T_(2) =2^(r-1) T_(1)`
`P_(3) =2^(r-1) P_(1)`