When a system is taken from a state `i` to a state `f` in Figure, along the path `iaf`, we find `DeltaQ=50cal` and `DeltaW=20cal` while during the path `ibf`, `DeltaQ=36cal`. If `U_i=10cal`.
(a) What is U?
What is `W` along the path `ibf`?
(c ) If `W=-13cal`, along the curved path `fi`, what is `DeltaQ` for this path?
(d) If `U_b=22cal`, what is `DeltaQ` for the process `ib`? for `bf`?

Explanation

`DeltaQ_(iaf)=50cal`,`DeltaW_(iaf)=20cal`,`DeltaQ_(ibf)=36cal`
`U_i=10cal`
(a) Path iaf: `DeltaU=U_f-U_k=U_f-10`
`DeltaQ=DeltaU+DeltaW`
`50=U_f-10+20impliesU_f=40cal`
(b) Path ibf: `DeltaU=U_f-U_i=40-10=30cal`
`DeltaQ=DeltaU+DeltaW`
`36-30+DeltaWimpliesDeltaW=6cal`
(c ) Path fi: `DeltaU=U_i-U_f=10-40=-30cal`
`DeltaQ=DeltaU+DeltaW=-30-13=-43cal`
Path ib: `DeltaU=U_b-U_i=22-10=12cal`
`DeltaQ=DeltaU+DeltaW=12+6=18cal`
`(DeltaW_(ib)=DeltaW_(ibf))`
Path bf: `DeltaU=U_f-U_b=40-22=18cal`
`DeltaQ=DeltaU+DeltaW=18+0=18cal`