When a system goes from state A to state B, it is supplied with 400 J of heat and it does 100 J of work.
(a) For this transition, what is the system's change in internal energy?
(b) If the system moves from B to A, what is the change in internal energy?
(c) If in moving from A to B along a different path in which `W_(AB)^'=400J` of work is done on the system, how much heat does it absorb?

Answer

A, B, C

Explanation

(a) From the first law,
`DeltaU_(AB)=Q_(AB)-W_(AB)=(400-100)J=300J`
Consider a closed path that passes through the state A and B. Internal energy is a state function so `DeltaU` is zero for a closed path.
Thus, `DeltaU=DeltaU_(AB)+DeltaU_(BA)=0` or `DeltaU_(BA)=-DeltaU_(AB)=-300J`
(c) The change in internal energy is the same for any path, so
`DeltaU_(AB)=DeltaU_B^'=Q_(AB)^'-W_(AB)^'`
`300J=Q_(AB)^'-(-400J)`
and the heat exchanged is `Q_(AB)^'=-100J`
The negative sign indicates that the system loses heat in this transition.