Question 2.4: When a system is taken from state a to state b in the accomp...
When a system is taken from state a to state b in the accompanying figure along path acb, 100 J of heat flows into the system and the system does 40 J of work.
(a) How much heat flows into the system along path aeb if the work done by the system is 20 J?
(b) The system returns from b to a alongpath bda. If the work done on the system is 30 J, does the system absorb or liberate heat? How much?
Assume that the system changes only in its internal energy and thus that Eq. (2.3) is applicable. For path acb, and thus for any path leading from a to b,
\Delta U^{t}_{ab} =Q_{acb} + W_{acb} = 100 − 40 = 60 J
(a) For path aeb,
\Delta U^{t}_{ab} =60 = Q_{aeb} + W_{aeb} = Q_{aeb} -20 and Q_{aeb} = 80 J
(b) For path bda,
\Delta U^{t}_{ba} = – \Delta U^{t}_{ab} = – 60 = Q_{bda} + W_{bda} = Q_{bda} + 30
and
Q_{bda} = − 60 − 30 = − 90 J
Heat is therefore transferred from the system to the surroundings.