The Vapor-Compression Cycle in Software

Encoding QR in Software The Vapor-Compression Cycle

W to the system Since AU of the working fluid is zero for the cycle, the first law is written:

The measure of the effectiveness of a refrigerator is its coeficient of performance w, defined as:

(92)

Equation (91) may be divided by I Qc I:

Combination with Eq (57) gives:

and Eq (92) becomes:

This equation applies only to a refrigerator operating on a Carnot cycle, and it gives the maximum possible value of w for any refrigerator operating between given values of TH and Tc It shows clearly that the refrigeration effect per unit of work decreases as the temperature of heat absorption Tc decreases and as the temperature of heat rejection TH increases For refrigeration at a temperature level of 27815 K (5 C) in a surroundings at 30315 K (30"C), the value of w for a Carnot refrigerator is:

The vapor-compression refrigeration cycle is represented in Fig 91 Shown on the T S diagram are the four steps of the process A liquid evaporating at constant pressure (line 1 + 2) provides a means for heat absorption at a low constant temperature The vapor produced is compressed to a higher pressure, and is then cooled and condensed with rejection of heat at a higher temperature level Liquid from the condenser returns to its original pressure by an expansion process In principle, this can be carried out in an expander from which work is obtained, but for practical reasons is accomplished by throttling through a partly open valve The pressure drop in this irreversible process results from fluid friction in the valve As shown in Sec 71, the throttling process occurs at constant enthalpy In Fig 91 line 4 -t 1 represents this throttling process The dashed line 2 + 3' is the path of isentropic compression (Fig 76) Line 2 --+ 3, representing the actual compression process, slopes in the direction of increasing entropy, reflecting inherent irreversibilities

On the basis of a unit mass of fluid, the equations for the heat absorbed in the evaporator and the heat rejected in the condenser are:

These equations follow from Eq (232) when the small changes in potential and kinetic energy are neglected The work of compression is simply:

and by Eq (92), the coefficient of performance is:

To design the evaporator, compressor,condenser, and auxiliary equipment one must know the rate of circulation of refrigerant m This is determined from the rate of heat absorption in the evaporate by the equation:

The vapor-compression cycle of Fig 91 is shown on a P H diagram in Fig 92 Such diagrams are more commonly used in the description of refrigeration processes than T S diagrams, because they show directly the required enthalpies Although the evaporation and condensation processes are represented by constant-pressure paths, small pressure drops do occur because of fluid friction

'1n the United States refrigeration equipment is commonly rated in tons of refrigeration; a ton of refrigeration is defined as heat absorption at the rate of 12 000 Btu h-' or 12 6522 kJ h-' This corresponds approximately to the rate of heat removal required to freeze 1 short ton [or 2000 (lb)] of water initially at 32 ( O F ) per day or remove 35145 kW at 27315 K (0 C)

For given values of Tc and T H ,the highest possible value of w is attained for Carnotcycle refrigeration The lower values for the vapor-compression cycle result from irreversible expansion in a throttle valve and irreversible compression The following example provides an indication of typical values for coefficients of performance

As shown in Sec 52, the efficiency of a Carnot heat engine is independent of the working medium of the engine Similarly, the coefficient of performance of a Carnot refrigerator is