Question

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 1

Thus the change in internal energy is − 100 J

Explanation:

(a) From the first law.

ΔU(AB) = Q(AB) − W(AB) = (400 − 100) J = 300 J

(b) Consider a closed path that passes through the state A and B. Internal energy is a state function so ΔU is zero for a closed path.

Thus, ΔU = ΔU(AB) + ΔU(BA) = 0

or ΔU(BA) = −ΔU(AB) = −300 J

(c) The change in internal energy is the same for any path, so

ΔU(AB) = ΔU′B = Q′AB − W′AB

300 J = Q′AB − (− 400 J)

and the heat exchanged is Q′AB= − 100 J

The negative sign indicates that the system loses heat in this transition.

Answer 2

$\huge \sf - 100 \: \: \: \mathfrak{joules}$