SECOND LAW OF THERMODYNAMICS
Thermodynamics
In the application of the first law general energy equation to a simple heat exchanger under
steady flow conditions, it is found that the mass flow rates and enthalpies of the two fluids are
related by the following relationship.
(1-36)
m1 (hout,1
hin,1)
m2 (hout,2
hin,2)
where:
= mass flow rate of the working fluid 1 (lbm/hr)
m1
= mass flow rate of the working fluid 2 (lbm/hr)
m2
h
out, 1
= specific enthalpy of the working fluid 1 leaving the heat exchanger (Btu/lbm)
h
in, 1
= specific enthalpy of the working fluid 1 entering the heat exchanger (Btu/lbm)
h
out, 2
= specific enthalpy of the working fluid 2 leaving the heat exchanger (Btu/lbm)
h
in, 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 component
efficiencies. In this section we will apply this information to allow us to compare and evaluate
various ideal and real cycles. This will allow us to determine how modifying a cycle will affect
the 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 source
and the temperature of the heat sink, it follows that to improve a cycles’ efficiency all we have
to 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 heat
sink. 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 or
the 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 the
boilers, and therefore they are limited to about 1500°F (1960°R) for a maximum heat
source temperature.
Using these limits to calculate the maximum efficiency attainable by an ideal Carnot cycle gives
the following.
h
TSOURCE
TSINK
TSOURCE
1960oR
520oR
1960oR
73.5%
HT-01
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