Carnot cycle refrigerator efficiency

The Carnot cycle is formulated directly from the second law of thermodynamics. It is a perfectly reversible, adiabatic cycle consisting of two constant entropy processes and two constant temperature processes. It defines the ultimate efficiency for any process operating between two temperatures. The coefficient of performance (COP) of the reverse Carnot cycle (refrigerator) is expressed as... 

Just as the Carnot cycle C of Fig. 4.3 can be claimed to be the most efficient possible heat engine ( reai < fcamot = 1 — c/ h )> so too can the reverse Carnot cycle C be claimed to be the most efficient possible refrigerator ... 

Estimate the annual cost of providing refrigeration to a condenser with duty 1.2 MW operating at —5°C. The refrigeration cycle rejects heat to cooling water that is available at 40 °C and has an efficiency of 80% of the Carnot cycle efficiency. The plant operates for 8,000 hours per year and electricity costs 0.06/kWh. 

The Carnot cycle is an ideal thermodynamic cycle that represents the most efficient cycle for a heat engine and refrigeration machine operating between two temperature limits. It consists of four reversible processes (1) reversible... 

A thermodynamic cycle describes a set of processes through which a system returns to the same state that it was in initially. Typically cycles are used to produce power or provide refrigeration. Since the system returns to its initial state after the cycle has been completed, aU the properties have the same values they had originally. The advantage of executing a thermodynamic cycle is that by having the system return to its initial state, we can repeat the cycle continuously. There are many different examples of thermodynamic cycles in this section, we examine one such cycle—the Carnot cycle.In Chapter 3, we will learn that a Carnot cycle represents the most efficient type of cycle we can possibly have. 

The COP of real refrigeration cycles is always less than the Carnot efficiency. It is usually about 0.6 times the Carnot efficiency for a simple refrigeration cycle, but can be as high as 0.9 times the Carnot efficiency if complex cycles are used. Good overviews of refrigeration cycle design are given by Dincer (2003), Stoecker (1998), and Trott and Welch (1999). 

The technical reasons for the unavoidable rejection of heat at the lower-temperature reservoir will become clearer when we consider actual cycles in Chanter 6. The fundamental reason, however, is evident in Figure According to eg. (4. o). the amount of heat Ql is equal in absolute value to the area DCC D. Clearly, it is impossible to complete the cycle without rejecting this amount of heat at the lower reservoir. The area is zero only if Tl is equal to absolute zero, and in this case the Carnot efficiency becomes i. For any other value of Tl, the amount of Ql is nonzero and the efficiency of the cycle less than i. In practice, Tl is fixed by the temperature of the ambient surroundings. It is possible of course to produce temperatures lower than ambient using refrigeration, but we will see in Chapter 6 that this requires work and cancels the benefit from the higher efficiency of the cycle. 

The efficiency of a refrigerator used to carry low-temperature heat from the coil anddeliver it at room temperature can be described in terms of the efficiency of an ideal (Carnot) refrigeration cycle, multiplied by a mechanical or process efficiency, which represents the effect of additional mechanical and thermal losses in the actual refrigeration system. 

We first encountered this relationship in Example 2.23. Equation (3.9) represents the highest efficiency that we can possibly have in operating between a hot reservoir at Th and a cold reservoir at Tc- To improve the efficiency further requires a hotter energy source or a colder energy sink. Similarly, we can use Equation (3.7) to write the coefficient of performance of a Carnot refrigeration cycle as ... 

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