Ideal and Lost Work For Open System

4.6 Ideal and Lost Work for Flow Systems
We next derive the expressions for work exchange between system and surroundings for an open system operating under steady state by incorporating the idea of irreversibility. As we have discussed earlier, mechanical irreversibilities lead to loss of work due to dissipative conversion to heat. Thus, if work is to be delivered by an open system the maximum work obtains when the processes are mechanically reversible, we call that ideal work. Conversely, when work is done on the system the ideal work provides the minimum work needed to change the fluid state between the inlet and the exit. This is because an extra work would need to be provided beyond the ideal work against mechanical dissipative forces.  From the considerations in the last section it may be evident that ideal work obtains when the processes associated with the open system are both internally and externally reversible. For such a case one may write eqn. 4.29 as follows: 
(4.30)
Thus: (4.31)
From the 1st Law applied to the ideal case:
(4.32)
Putting eqn. 4.31 into 4.32 and simplifying (assuming negligible kinetic and potential energy changes):
(4.33)
Or: (4.34)
In real processes however, actual work involved will depend on the extent of associated irreversibilities; hence we define lost work as follows:
(4.35)
Now from eqn. 4.32 for the simplest case where kinetic and potential energy changes are negligible: 
(4.36)
Using eqns. 4.34 and 4.35: 


Applying eqn. 4.30, to a real process: (4.38)
Or:                       (4.39)
We next derive the expressions for work exchange between system and surroundings for an open system operating under steady state by incorporating the idea of irreversibility. As we have discussed earlier, mechanical irreversibilities lead to loss of work due to dissipative conversion to heat. Thus, if work is to be delivered by an open system the maximum work obtains when the processes are mechanically reversible, we call that ideal work. Conversely, when work is done on the system the ideal work provides the minimum work needed to change the fluid state between the inlet and the exit. This is because extra work would need to be provided beyond the ideal work to against mechanical dissipative forces.  From the considerations in the last section it may be evident that ideal work obtains when the processes associated with the open system are both internally and externally reversible. For such a case one may write eqn. 4.29 as follows:

Thus from eqns. 4.37 and 4.39 it follows that:
(4.40) 
Eqn. 4.40 suggests that greater the entropy generation rate  due to process irreversibility, greater is the lost work. Since irreversibilities implicit in a process cannot be calculated theoretically, it is indirectly expressed by a process efficiency factor, . The expression for such efficiency is as follows. 
                   .                                  (4.41)
(4.42)
(4.37)