SECOND LAW OF THERMODYNAMICS ThermodynamicsIn the application of the first law general energy equation to a simple heat exchanger understeady flow conditions, it is found that the mass flow rates and enthalpies of the two fluids arerelated by the following relationship.(1-36)m_{1} (h_{out,1}h_{in,1})m_{2} (h_{out,2}h_{in,2})where:= mass flow rate of the working fluid 1 (lbm/hr)m_{1}= mass flow rate of the working fluid 2 (lbm/hr)m_{2}hout, 1= specific enthalpy of the working fluid 1 leaving the heat exchanger (Btu/lbm)hin, 1= specific enthalpy of the working fluid 1 entering the heat exchanger (Btu/lbm)hout, 2= specific enthalpy of the working fluid 2 leaving the heat exchanger (Btu/lbm)hin, 2= specific enthalpy of the working fluid 2 entering the heat exchanger (Btu/lbm)In the preceding sections we have discussed the Carnot cycle, cycle efficiencies, and componentefficiencies. In this section we will apply this information to allow us to compare and evaluatevarious ideal and real cycles. This will allow us to determine how modifying a cycle will affectthe cycle’s available energy that can be extracted for work.Since the efficiency of a Carnot cycle is solely dependent on the temperature of the heat sourceand the temperature of the heat sink, it follows that to improve a cycles’ efficiency all we haveto do is increase the temperature of the heat source and decrease the temperature of the heat sink.In the real world the ability to do this is limited by the following constraints.1. For a real cycle the heat sink is limited by the fact that the "earth" is our final heatsink. And therefore, is fixed at about 60°F (520°R).2. The heat source is limited to the combustion temperatures of the fuel to be burned orthe maximum limits placed on nuclear fuels by their structural components (pellets,cladding etc.). In the case of fossil fuel cycles the upper limit is ~3040°F (3500°R).But even this temperature is not attainable due to the metallurgical restraints of theboilers, and therefore they are limited to about 1500°F (1960°R) for a maximum heatsource temperature.Using these limits to calculate the maximum efficiency attainable by an ideal Carnot cycle givesthe following.hT_{SOURCE}T_{SINK}T_{SOURCE}1960^{o}R520^{o}R1960^{o}R73.5%HT-01 Page 84 Rev. 0