Heat pump. Table des matières. Matthieu Schaller et Xavier Buffat 10 mai 2008.

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1 Heat pump Matthieu Schaller et Xavier Buffat 10 mai 2008 Table des matières 1 Introduction 2 2 Theory General principle The heat pump Mollier s diagramm Results and discussion System s evolution Efficiency Mollier graphic Conclusion 6 5 Apendix 8 1

2 1 INTRODUCTION 2 1 Introduction Nowadays the developpement of new energy source and the research in optimisations are two very important parts of physics. The heat pump is a machine that is very often used to produce electricity or to heat up a house. The increase of efficiency of such a pump is a central point. In this work we are going to study a heat pomp and going to try to determinate its caracteristics. 2 Theory 2.1 General principle If you bring in contact two heat sources at different temperatures T 1 > T 2 you will observe a heat flow from the first source to second accordingly to the second principle of thermodynamics. After a long time, the two sources will have the same temperature T f. If you want to reverse this evolution you must produce some work in order to bring heat from the cold source to the hot source. Fig. 1 The heat pump principle of work In order to measure the efficiency of suc a machine, we use the definition of the coefficient of performance ɛ which is given by : ɛ = δq 2 δw (2.1)

3 3 RESULTS AND DISCUSSION 3 where the different symbols refere to figure 1. The Carnot-Cycle s theory gives a theoretical value for this coefficient : ɛ th = T 1 T 2 T 1 (2.2) In this experiment, we are going to measure this coefficient and see if it s near of the theoretical value. 2.2 The heat pump A heat pump uses a fluid (for us it s Freon 12) to get and release some heat in the both sources. When this fluid evaporates, he gets heat from his environnement and when he condenses, he gives the same heat around itself. In ordrer to get the fluid evaporate en condense you need to compress and to release it. This done by an electrical pump which actually is the source of work δw. 2.3 Mollier s diagramm The key point for a heat pump is the choice of the fluid. The best way to choose the fluid is to use Mollier s diagramm. It represents the logarithm of the gas pressure as a function of it s enthalpy. During the experiment, we measure the condensation pressure P cond and the pressure of evaporation P evap. We also need the three different temperatures ; the evaporation temperauture T 3, the condensation temperature T 1 and the liquid temperature T 2. With these five values, you can draw the thermodynamic s cycle on the diagramm. You can then read the different enthalpy values on the diagramm and get the maximal coefficient of performance for this fluid, which is given by : ɛ max = h 2 h 3 h 2 h 1 (2.3) We are going to measure this maximal coefficient of performance. 3 Results and discussion During the whole experiment, the pump is powered by the electrical communication with these caracteristics : U I P = UI 235 ± 0.1 V 0.86 ± 0.01 A ± 2.5 W

4 3 RESULTS AND DISCUSSION 4 Fig. 2 Temperature of the two bacs while heat pump is running. (1) and (2) indicates the first and second experiment and (3) the experiment with the cold source at constant temperature. 3.1 System s evolution The figure 2 summarize the experiments, it represents the evolution of the temperature measured in the bacs while the heat pump is running. We can see the differences between the three experiments. We supposed for the calculations that the system would finally stays in a stationnary state, the graphic shows that this state is never reached. Indeed, the insulation of the two bacs are quiet good, thus the pump can increase the difference of temperature between the bacs and the environement until the insulation let more heat get in that the pump can handle. Obviously, the stationnary state would take place with temperature very high for the warm source, and very cold for the cold source, most likely below water freezing temperature. The machine can not handle the water to solidify, preventing the experiment to be carried out fully. Although, we suppose that the final state reached is close to the stationnary one. The temperature is very high at the begining and decrease while time is running. This is due to the fact that the temperature difference increase, thus it needs more and more energy to take heat from the cold source to warm source. According to the theorectical efficiency equation, this efficiency decrease while temperature difference increase, and thus we can assume that the effective efficiency goes the same way. 3.2 Efficiency

5 3 RESULTS AND DISCUSSION 5 Fig. 3 Efficiency of the pump. The pump is cold at the begining. First experiment Figure 3 shows the evolution of efficiency functions of time. It is important to notice that the experimental efficiency is mostly constant during the experiment. By zooming in, it appears that it is slowly decreasing in time. The experimental efficiency is way lower than the theoretical one at the begining, the difference decrease quickly to zero. It apparears that the experimental efficiency gets higher than the theoretical one, which is completly absurd. This is due to the measure s error, assuming a half degree margin on the temperature measure, the error is about 25%. Then we assume that the difference is due to this error, nevertheless it shows that the experimental efficiency is very close to the theorectical one. Second experiment Figure 4 represents the evolution of efficiency for the experiment (2) and (3). The fact that the pump is warm from the begining make the experimental efficiency closer to the theoretical one from the begining, but does not really change the efficiency. Infinite heat source It is important to notice on figure 4 that both theoretical and experimental efficiency are higher using an infinite heat source. This is due to the fact that the temperature of the cold source remain constant. Consequently, the difference of temperature increase significantly slower than with a finite quantity of water. We deduce from this observation that the best way to use this kind of machine is to use a big reserve of heat to have maximum efficiency. For example, EPFL, is using a heat pump to heat the building which use the lake as a infinitermal source.

6 4 CONCLUSION 6 Fig. 4 Efficiency of the pump. The pump is warm at the begining, for experiment (2) and (3) 3.3 Mollier graphic Using Mollier graphics, we deduce the specific enthalpy of the different states of the fluid. We find : h ± 10 h ± 10 h ± 10 Which gives the performance maxium that could be reach with the forane 12, ɛ = 10.6 ± 0.6. This is way higher than the efficiency found above. this is not astonishing, considering all the unexpected outflows and mechanical wasted energy that are not considered in the calulation of this value. 4 Conclusion This experiment shows the caracteristics of heat pump, it allows to see that, even with a quiet low efficieny, the heat provided by the pump is way higher than the electric power given to heat, making this kind of machine very attractive to heat buildings using outer heat.

7 4 CONCLUSION 7

8 5 APENDIX 8 5 Apendix The pump is cold at the begining t P 1 P 2 T in T e T out T 1 T

9 5 APENDIX 9 The pump is hot from the begining t P 1 P 2 T in T e T out T 1 T Cold source stays at constant temperature t P 1 P 2 T in T e T out T 1 T

Lecture Outline Chapter 18. Physics, 4 th Edition James S. Walker. Copyright 2010 Pearson Education, Inc.

Lecture Outline Chapter 18. Physics, 4 th Edition James S. Walker. Copyright 2010 Pearson Education, Inc. Lecture Outline Chapter 18 Physics, 4 th Edition James S. Walker Chapter 18 The Laws of Thermodynamics Units of Chapter 18 The Zeroth Law of Thermodynamics The First Law of Thermodynamics Thermal Processes