The entropy balance for a control volume at steady state is
It is assumed that there is no heat transfer between the pipes and the surroundings. That means no entropy flows in or out of the control volume associated with the heat transfer. The control volume has electric work input, but the work is entropy free. Hence, the entropy balance for this steady-flow control volume can be simplified as
Since water enters the T-elbow and the electric heater at the same temperature,
s_{1} = s_{2}
Also, with the mass balance, the entropy generation can be determined by
Hence, a 15-minute shower will generate entropy
S_{gen} = (15)(60)(58.1) = 52,290 J/K = 52.3 kJ/K |