In the process shown below, which of the following option is correct ?

Options

A. `DeltaQ_(AB)=+ve`, `DeltaQ_(BC)=+ve`, `DeltaQ_(CA)=+ve`
B. `DeltaQ_(AB)=+ve`, `DeltaQ_(BC)=-ve`, `DeltaQ_(CA)=+ve`
C. `DeltaQ_(AB)=+ve`, `C_(BC)=oo`, `(dT)/(dP)=+ve` for `AB`
D. `DeltaQ_(AB)=+ve`, `DeltaQ_(BC)=-ve`, `DeltaQ_(CA)=-ve`

Explanation

For process `AB`
`P=(VP_(0))/(V_(0))rArr T=(PV)/(nR)=(P)/(nR)(2V)/(P_(0))`
`(dT)/(dP)=(2P)/(nR)(V_(0))/(P_(0))`
`(dT)/(dP)=(4V_(0))/(nR)` at `B`.
Since `T` goes on increasing, `DeltaW` is positive,
`DeltaQ_(AB)=+ve`
For `BC`
`P(2V_(0))=nRTrArrT=(2PV_(0))/(nR)`
`(dT)/(dP)=(2V_(0))/(nR)` at `B`
`:. (dT)/(dP)` is not defined at `B`.
In `BC` temperature goes on decreasing.
`:. DeltaQ_(BC)` is `-ve`.
For `CA`
`DeltaW= -ve`
`:. Q_(CA)=-ve`