Carnot cycle equation

That is to say, the entropy of the thermodynamic system represented by die working gas returns to its original value when it passes through a Carnot cycle. Equation (9) is valid for any reversible cyclical process. 

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. 

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 ... 

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... 

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... 

We prove the identity of the Kelvin scale and the ideal gas scale by using an ideal gas as the fluid in a reversible heat engine operating in a Carnot cycle between the temperatures T2 and 7. An ideal gas has been defined by Equations (2.36) and (2.37). Then the energy of an ideal gas depends upon the temperature alone, and is independent of the volume. 

Considerations from the classic Carnot cycle define AS as Q/T and Q = TAS. Substituting this relationship into Equation (2.4) and substituting AG for W, we obtain Equation (2.3), AG = AH - TAS. 

The value of Qh / QcI given by this equation is of course a minimum, becau Carnot cycles cannot be achieved in practice. 

Ideal gas, 61, 63-77 Carnot cycle for, 145-147 equation of state for, 64 entropy changes for, 152-155 fugacity of, 327, 334 heat capacity of, 64-68, 107-113 internal energy and enthalpy changes for, 64-77... 

The valueof 2h / 2c I given by tliis equation is of course a minimum, because Carnot cycles camrotbe acliieved in practice. 

The above equation states that the sum of the Q/T ratio along a Carnot cycle is zero. In general, any closed cycle, starting at some point and moving along reversible paths and returning to the starting point, can be represented by many small isothermal and adiabatic steps. The heat transferred in the adiabatic steps is, by definition, zero. For all the isotherms contained in the loop, the summation of the heat absorbed in each isotherm divided by its absolute temperature is zero ... 

The efficiency of the cycle is defined to be the fraction of the heat absorbed at the high temperature that is converted into work, -W)IQx. By combining Equation (4.37) and Equation (4.38), the efficiency of the Carnot cycle is obtained. 

The efficiency of the ideal-gas Carnot cycle is found upon substituting Equation (4.43) into Equation (4.42),... 

The ideal-gas Carnot cycle is a particular case of the Carnot cycle its efficiency must be given by the general formula of Carnot cycles. Comparison of Equation (4.45) with Equation (4.40) shows... 

From equation (5.22) for the efficiency of a reversible Carnot cycle, it follows that... 

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