Carnot equation

The ideal mechanical power requirement of a thermocompression evaporator is given by the Carnot equation ... 

Expansion and Exit Losses For ducts of any cross section, the frictional loss for a sudden enlargement (Fig. 6-13c) with turbulent flow is given by the Borda-Carnot equation ... 

The father of thermodynamics is Sadi Carnot. He wrote Reflections on the Motive Power of Fire in 1824. This was a discourse on heat, power, and engine efficiency. The Carnot engine, Carnot cycle, and Carnot equations are named after him. 

As an inevitable consequence of the thermodynamics described by the Carnot equation, engines that convert heat to mechanical energy cannot utilize much of the heat, and the waste heat is carried away by an engine cooling system. Typically, a small portion of this heat is used in automotive heaters on cold days. On a broader scale, such as municipal electrical systems, this heat can be used for heating buildings. Such efficiencies are discussed in Section 17.19. 

Considering the Carnot equation and common means for energy conversion, what might be the role of improved materials (metal alloys and ceramics) in ino-easing energy conversion efficiency ... 

The second law of thermodynamics was actually postulated by Carnot prior to the development of the first law. The original statements made concerning the second law were negative—they said what would not happen. The second law states that heat will not flow, in itself, from cold to hot. While no mathematical relationships come directly from the second law, a set of equations can be developed by adding a few assumptions for use in compressor analysis. For a reversible process, entropy, s, can be defined in differential form as... 

The exergy equation (2.26) enables useful information on the irreversibilities and lost work to be obtained, in comparison with a Carnot cycle operating within the same temperature limits (T ,ax = Ey and T in = To). Note first that if the heat supplied is the same to each of the two cycles (Carnot and IJB), then the work output from the Carnot engine (Wcar) is greater than that of the IJB cycle (Wijg), and the heat rejected from the former is less than that rejected by the latter. 

The maximum possible efficiency at which a heat engine can work is defined by the Carnot efficiency equation E = (T2—Tl)/T2, where E is the efficiency of the heat engine, T1 is the temperature of the cold... 

Because the gas in the Carnot cycle starts and ends at the same state, the system s entropy does not change during a cycle. Now apply the second law to the universe for the case of the Carnot cycle. Because the processes are reversible, the entropy of the universe does not change by Equation 2b. This can be written ... 

In the operations constituting a Carnot s cycle, changes of Q and T occur separately. In the majority of cases both these changes occur together, so that the temperature of the working substance may be regarded as a function of the time. Equation (4) therefore requires extension, and this was effected by Lord Kelvin in May, 1854, in the following way ... 

In 1879 Lord Kelvin introduced the term nwtivity for the possession, the waste of which is called dissipation at constant temperature this is identical with Maxwell s available energy. He showed in a paper On Thermodynamics founded on Motivity and Energy Phil. Mag., 1898), that all the thermodynamic equations could be derived from the properties of motivity which follow directly from Carnot s theorem, without any explicit introduction of the entropy. 

This approximation improves as we take more and more, smaller and smaller, Carnot cycles, until in the limit of an infinite number of infinitesimal cycles, the agreement is exact. When this occurs, the sum in equation (2.36) is replaced by an integral over the cycle. That is,... 

In the next chapter, we will return to the Carnot cycle, describe it quantitatively for an ideal gas with constant heat capacity as the working fluid in the engine, and show that the thermodynamic temperature defined through equation (2.34) or (2.35) is proportional to the absolute temperature, defined through the ideal gas equation pVm = RT. The proportionality constant between the two scales can be set equal to one, so that temperatures on the two scales are the same. That is, 7 °Absolute) = T(Kelvin).r... 

Substitution for K4 jVy from this equation into equation (3.84) and dividing by <72 given by equation (3.79) gives the efficiency 77 of conversion of heat into work for the Carnot cycle as... 

This equation was originally arrived at by the French Engineer Sadi Carnot in 1824 during his investigation on the efficiency of heat engines. In terms of the heat and the entropy changes in the system, the second law may be expressed as follows ... 

In this form, it appears that the allowable A T increases as the working fluid temperature increases. This suggests that the optimum AT for a heat source at 900°R is lower than that for a heat source at 1100°R. In fact, Equation (j) indicates that the optimum AT is directly proportional to 7. Sama argues that this is somewhat counterintuitive because the Carnot value of a high-temperature source implies using a smaller A T to reduce lost work. 

Carnot efficiency of, 24 654 thermodynamics of, 24 653-654, 655 Heaters, feedwater, 23 218 Heat exchange, 10 144 Heat exchanger design equation, 13 189 Heat-exchanger effectiveness method,... 

Equation (6.16), which includes Equation (6.6), is a mathematical statement of Carnot s theorem ... 

Now consider a group of three heat reservoirs at temperatures fj < 2 < h and a reversible Carnot engine that operates successively between any pair of reservoirs. According to Equation (6.19)... 

As the isothermal steps in the Carnot cycle are the only steps in which heat is exchanged, we also can write Equation (6.47) as... 

If we integrate Equation (6.49) for the steps of a reversible Carnot cycle, the results are... 

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