Heat Rejection

Figure 29 Carnot Cycle vs. Typical Power Cycle Available Energy

Thermodynamics Heat Transfer and Fluid Flow Volume 1 of 3
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Thermodynamics SECOND LAW OF THERMODYNAMICS This calculation indicates that the Carnot cycle, operating with ideal components under real world constraints, should convert almost 3/4 of the input heat into work. But, as will be shown, this ideal efficiency is well beyond the present capabilities of any real systems. Heat Rejection To understand why an efficiency of 73% is not possible we must analyze the Carnot cycle, then compare the cycle using real and ideal components. We will do this by looking at the T-s diagrams of Carnot cycles using both real and ideal components. The energy added to a working fluid during the Carnot isothermal expansion is given by q_s. Not all of this energy is available for use by the heat engine since a portion of it (q_r) must be rejected to the environment. This is given by: q_r = T_o Ds in units of Btu/lbm, (1-37) where T_o is the average heat sink temperature of 520°R. The available energy (A.E.) for the Carnot cycle may be given as: A.E. = q_s - q_r. (1-38) Substituting equation 1-37 for q_r gives: A.E. = q_s - T_o Ds in units of Btu/lbm. (1-39) and is equal to the area of the shaded Figure 28 Carnot Cycle region labeled available energy in Figure 28 between the temperatures 1962° and 520°R. From Figure 28 it can been seen that any cycle operating at a temperature of less than 1962°R will be less efficient. Note that by developing materials capable of withstanding the stresses above 1962°R, we could greatly add to the energy available for use by the plant cycle. From equation 1-37, one can see why the change in entropy can be defined as a measure of the energy unavailable to do work. If the temperature of the heat sink is known, then the change in entropy does correspond to a measure of the heat rejected by the engine. Rev. 0 Page 85 HT-01

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