Carnot engine heat pump

Fig. 1. Schematic representation of (a) Carnot heat engine and (b) Carnot refrigerator used as a heat pump.

Tc- This may require Carnot engines or heat pumps internal to the system that provide for the reversible transfer of heat from the temperature of the flowing fluid to that of the surroundings. Since Carnot engines and heat pumps are cychc, they undergo uo net change of state. 

The above analysis has been concerned with heat transfer from the control volume. Consider next heat [AQ] = [d REvlx transferred to the control volume. Then that heat could be reversibly pumped to CV (at temperature T) from the atmosphere (at temperature To) by a reversed Carnot engine. This would require work input... 

Here Tc is the temperature of the cooling reservoir, i.e. the surroundings, while Th is the temperature of the process, i.e. the temperature of combustion. The Carnot efficiency is applicable for conventional heat pump engines. Efficiencies of more than 100 % correspond to converting heat from the surroundings into electricity and is only of academic interest, as is the high efficiency listed in Tab. 8.10. 

Figure 6.1. Scheme of a Carnot engine as a) a heat engine and b) as a refrigerator or 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. 

A Carnot engine with a steady flow rate of 1 kg/sec uses water as the working fluid. Water changes phase from saturated liquid to saturated vapor as heat is added from a heat source at 300° C. Heat rejection takes place at a pressure of lOkPa. Determine (1) the quality at the exit of the turbine, (2) the quality at the inlet of the pump, (3) the heat transfer added in the boiler, (4) the power required for the pump, (5) the power produced by the turbine, (6) the heat transfer rejected in the condenser, and (7) the cycle efficiency. 

The Carnot cycle is a reversible cycle. Reversing the cycle will also reverse the directions of heat and work interactions. The reversed Carnot heat engine cycles are Carnot refrigeration and heat pump cycles. Therefore, a reversed Carnot vapor heat engine is either a Carnot vapor refrigerator or a Carnot vapor heat pump, depending on the function of the cycle. 

The clockwise direction in C corresponds to the clockwise direction in the Carnot cycle, with heat and work input/output as shown in Fig. 4.2. We can similarly envision a reverse Carnot engine ( heat pump ) C, which is obtained by reversing the directions of heat and work arrows and traversing the Carnot cycle in counterclockwise direction ... 

With the improved C in hand, we can now envision operating the old Carnot cycle as a heat pump C, then coupling this to C as shown in (4.15), using the heat output qh from heat pump C, to drive the improved heat engine C (i.e., with qh = gj ) ... 

The thermal efficiency of this cycle is that of a Carnot engine, given by (5.8). As a reversible cycle, it could serve as a standard of comparison for actui steam power plants. However, severe practical difficulties attend the operatk of equipment intended to carry out steps 2 3 and 4 1. Turbines that take i saturated steam produce an exhaust with high liquid content, which causes sevel erosion problems, t Even more difficult is the design of a pump that takes in mixture of liquid and vapor (point 4) and discharges a saturated liquid (poll 1). For these reasons, an alternative model cycle is taken as the standard, at lei for fossil-fuel-buming power plants. It is called the Rankine cycle, and diSei from the cycle of Fig. 8.2 in two major respects. First, the heating step 1 2 ... 

Calorimeter, flow, 33-35, 117 Carnot cycle, 141-148, 248-250, 274-276 for power plants, 250 for refrigeration, 275-276 See also Heat engine Heat pump)... 

Note that if the Carnot heat engine is operated as shown in Fig. 4.3-2 it absorbs heat from the high-temperamre bath, exhausts heat to the low-temperature bath, and produces work. However, if the engine is operated in reverse, it accepts work, absorbs heat from the low-temperature bath, and exhausts heat to the high-temperature bath. In this mode it is operating as a refrigerator, air conditioner, or heat pump. 

Suppose we run the Carnot engine in reverse, as a refrigerator, but instead of having the interior of the refrigerator serve as the cold reservoir we use the outdoors as the cold reservoir and the interior of the house as the hot reservoir. Then the refrigerator pumps heat, Q2, from outdoors and rejects heat, — 6u the house. The coefficient of performance of the heat pump, is the amount of heat pumped into the high temperature... 

Two systems ( ) and ("), not necessarily reservoirs, but big systems, can be thermally coupled by a Carnot cycle. This is in practice a heat pump, or if it runs in the reverse direction, a heat engine. In this case, we have S + S" = 0, thus if the systems are big, for one revolution of the Carnot cycle d5 -I- d5" = 0. This constraint does not imply that T = T". Namely, the Carnot engine is an active device that releases or donates energy. In the Carnot engine, the change of entropy S is not directly connected with the change of entropy S", even when the cross balance d5 -F d5" = 0 over a full turn holds. 

The vapor-compression cycle was first used by French engineer Nicolas Leonard Sadi Carnot in 1824. Then in 1832, American inventor Jacob Perkins was the first to demonstrate a compression cooling technology that used ether as a refrigerant. But it was in 1852 that Scottish engineer William Thomson, also known as Lord Kelvin, conceptualized the first heat pump system, dubbed the heat multiplier. ... 

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. 

Could the efficiency of the Carnot engine be different from the efficiency the heat pump would have when run in reverse as a Carnot engine If so, either the supersystem is an impossible Clausius device as shown in Fig. 4.7(b), or the supersystem operated in reverse (with the engine and heat pump switching roles) is an impossible Clausius device as shown in Fig. 4.7(d). We conclude that all Carnot engines operating between the same two temperatures have the same efficiency. 

Solution The ideal heat pump is the Carnot engine running in reverse, i.e. it uses work to pump heat from a lower temperature to a higher temperature. For an ideal pump gi/Ti = Q2/T2.liQ = lOOJ, r2 = 293Kandri =276K,we obtain... 

If the above engine is run backward, one deals with a refrigerator or heat pump by performance of work, heat is extracted from the cold junction and delivered to the hot reservoir. Here it is sensible to introduce the figure of merit or ideal heating efficiency as QhfW = Tq/Tq Tq, the inverse of the Carnot efficiency derived above. The above ratio is rendered larger, the smaller the temperature difference between the hot and cold reservoir. See also Query 1, below. 

Carnot engine. If the amount of heat Q2 extracted at the low temperature T2 is pumped by supplying an amount of work (—IVj) to a higher temperature Ti where the amount of heat rejected is Qi, then ... 

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. 

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