General Expressions for Heat and Work

2 we combined the first and second laws to eliminate Q and W and thereby obtained forms of the fundamental equation those forms all contain some conceptual, such as U, S, or G. But as engineers we more often need values for heat and work rather than for changes in conceptuals. Unfortunately we cannot devise a purely theoretical scheme for computing the heat and work requirements for a real process every real process involves irreversibilities, and the magnitudes of those irreversibilities must either be measured or estimated. Usually such measurements or estimates are made relative to reversible changes, so we need to be able to compute the heat and work that accompany reversible changes. The necessary equations are derived here. 

Here AS p is defined analogously to (3.6.4). In general the entropy generation term is unknown, but if we consider reversible changes, then = 0, and (3.7.1) reduces to 

For this to apply, the external temperature Text must either equal the system temperature T and all stream temperatures and Tp, or there must be reversible means for transferring heat across any finite temperature difference. For real processes, the amount of heat given by (3.7.2) will boxmd the actual heat requirements an upper bound if heat is added to the system (SQ g, 0), a lower bound if heat is removed (SQret 0). 

In the special case of workfree processes with negligible kinetic and potential energy changes, the heat can be obtained from the overall energy balance (3.6.7), 

In workfree processes, the heat given by (3.7.3) is the actual heat 6Qgj.(, regardless of the reversibility of the process. 

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