One mole of a perfect gas is put through a cycle consisting of the following three reversible steps:

`(CA)` isothermal compression from `2` atm and `10` litre to `20 atm` and `1` litre.
`(AB)` Isobaric expansion to return the gas to the original volume of `10` litre with `T` going from `T_(1)` to `T_(2)`.
`(BC)` Cooling at constnat volume to bring the gas to the original pressure and temperature. the steps are shown schematically in the figure shown.
(a) Calculate `T_(1)` and `T_(2)`.
(b) Calculate `DeltaU,q` and `W` in calories, for each step and for the cycle.

Answer

(a) `T_(1)=243.60 K, T_(2)=2436.0 K`
(b) in path `CA,W=+1122.02 cal, DeltaU=0, q=w`
in path `AB,W=-4384.9 cal,DeltaU=+6577.2 cal`,
`q=10962.1 cal`
in path `BC,W=0,q=DeltaU=-6577.2;`