Carnot heat pump

If the Carnot cycle for a heat engine is carried out in the reverse direction, the result will be either a Carnot heat pump or a Carnot refrigerator. Such a cycle is shown in Fig. 1.5. Using the same graphical explanation that was used in the Carnot heat engine, the heat added from the low-temperature reservoir at Tl is area 1-4-5-6-1 g4i is the amount of heat added to the Carnot cycle from a low-temperature thermal reservoir. 

Referring to Fig. 1.5, the system undergoes a Carnot heat pump or Carnot refrigerator cycle in the following manner ... 

The COP (coefficient of performance) of the Carnot heat pump (or refrigerator) operating between a fixed high-temperature thermal reservoir at Tfi and a fixed low-temperature thermal reservoir at Tl is irrespective of the working substance. 

A schematic diagram of the Carnot refrigerator or Carnot heat pump is illustrated in Fig. 6.1. 

Figure 6.1 Carnot refrigerator or Carnot heat pump. 

Does the area enclosed by the Carnot heat pump cycle on a T-s diagram represent the network input for the heat pump ... 

Does the Carnot heat pump cycle involve any internal irreversibilities ... 

Wu, C., Specific heating load of an endo-reversible Carnot heat pump. 

Chen, L. and Wu, C., Optimal performance of an endo-reversible Carnot heat pump. Energy Conversion and Management, 38(14), 1439-1444, 1997. 

The only irreversibility is the transfer of heat from the water as it cools from 70 to 32 degF to the cold reservoir of the Carnot heat pump at 70 degF. 

Solution The procedure here is to calculate the maximum possible work Wideal which cap be obtained from 1 kg of steam in a flow process as it undergoes a change in state from saturated steam at 100°C to liquid water at 0°C. Now the problem reduces to the question of whether this amount of work is sufficient to operate a Carnot heat pump delivering 2,000 kJ as heat at 200°C and taking heat from the unlimited supply of cooling water at 0°C. 

If this amount of work, the maximum obtainable from the steam, is used to derive a Carnot heat pump operating between the temperatures of 0 and 200°C, the heat transferred at the higher temperature is... 

The energy transfers involved in one cycle of a Camot engine are shown sehematieally in Fig. 4.5(a). When the cycle is reversed, as shown in Fig. 4.5(b), the deviee is eaUed a Carnot heat pump. In each cycle of a Carnot heat pump, gh is negative and qc is positive. Since each step of a Carnot engine or Carnot heat pump is a reversible process, neither device is an impossible device. 

We will be able to reach an important conclusion regarding efficiency by considering a Carnot engine operating between the temperatures Tb and Tc, combined with a Carnot heat pump operating between the same two temperatures. The combination is a supersystem, and one cycle of the engine and heat pump is one cycle of the supersystem. We adjust the cycles of the engine and heat pump to produce zero net work for one cycle of the supersystem. 

Figure 3.3 The Path of the State Point in the V-T Pianeduring a Carnot Heat Pump Cycie.

A Carnot heat pump is a Carnot heat engine that is driven backwards by another engine. It removes heat from the cool reservoir and exhausts heat into the hot reservoir. Figure 3.3 represents a Carnot heat pump cycle, which is the reverse of the cycle of Figure 3.2. The steps are numbered with a prime ( ) and are numbered in the order in which they occur. Since we are considering the same Carnot engine run backwards,... 

The Carnot efficiency is always smaller than unity, so the Carnot heat pump coefficient of performance is always greater than unity. The amount of heat delivered to the hot reservoir is always greater than the work put into the heat pump because some heat has been transferred from the cold reservoir to the hot reservoir. There is no violation of the Clausius statement of the second law because the heat pump is driven by another engine. A real heat pump must have a lower coefficient of performance than a reversible heat pump but can easily have a coefficient of performance greater than unity. 

From Eq. (3.1-10) the amount of heat put into the hot reservoir by the Carnot heat pump is equal to... 

For Carnot heat pumps the coefficient of performance is always greater than unity, and for Carnot refrigerators the coefficient of performance exceeds unity if T /Tc < 2. 

Calculate the coefficient of performance of a Carnot heat pump operating between a high temperature of 70.0 F and a low temperature of 40.0 F. 

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