Thermal Energy Exercises

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Summary Understanding laws of thermodynamics is fundamental to understanding the workings of the universe. In this chapter we covered these laws and their relevance in designing useful thermal devices. In describing the working principle of such devices (a thermal power plant, a heat engine, a refrigerator, or any other thermodynamic system for that matter) we concluded that: 1) At least two reservoirs, one at a high temperature and the other at a low temperature, are needed. This is one of the important consequences of the second law of thermodynamics, which states that we cannot convert heat to work with a single heat source. In the case of a steam power plant, the steam generator and condenser are the two reservoirs. In internal combustion engines, the two heat reservoirs are hot combustion gases and cold exhaust gases. 2) Some form of energy is always needed to provide heat to the high-temperature heat reservoir. For power plants, energy needed to heat water comes from an external source Energy Boosters Mathematical Interlude ... In line with the definition proposed for thermal efficiency of heat engines for refrigerators and heat pumps, it is most convenient to define efficiency in terms of the desired effect (cooling or heating) as compared to the work that is necessary to achieve this effect. For a Carnot heat pump and refrigerator, the following results are obtained: TL and TH are temperatures of cold and hot reservoirs and must be expressed in the Kelvin scale. Of course, construction of such devices is not practical because there are always friction and conduction losses that cannot be completely eliminated. Example: A heat pump is to be used to heat a house during the winter to 20oC (293 K). The house loses heat at a rate of 100,000 kJ/h when the outside temperature drops to -8oC (265 K). What is the minimum power required to drive this heat pump? Solution: Minimum power usage can be achieved when the heat pump works reversibly as a Carnot heat pump. The COP of this heat pump would be: COP = 293/(293-265) = 10.5. That means for each unit of power consumed, 10.5 units of heat can be supplied to the room. The power input to the compressor is then 100,000/10.5 = 9556 kJ/h (or 2.7 kW). If the house was going to be heated by an electric resistance heater instead, we would have needed 10.5x2.7 = 28.35 kW of electric power. This example shows that by investing a small amount of work in a heat pump we can supply a great amount of heat. For this reason, heat pumps can be appropriately called “energy boosters”. C OP ideal, HP =COP ideal, R =THTH - TLTLTH - TL (i) (ii) 110 which could be fossil, nuclear, or less commonly solar or geothermal. 3) To increase efficiency, we must either increase the temperature of the source or lower the temperature of the sink. We are limited to atmospheric temperatures for the sink, but we can increase the source temperature. In power plants, we can raise steam temperature by increasing the boiler pressure (water boils at a higher temperature if the pressure is greater). Raising the compression ratio, minimizing heat losses, and using better fuels can similarly increase internal combustion efficiency. 4) Higher efficiencies not only reduce fuel consumption, but also protect our environment by producing fewer pollutants. In addition, higher efficiency means a smaller fraction of energy must be disposed of as waste heat, commonly termed “thermal pollution,” which is a major source of global warming. Additional Information Books 1. El-Sayed, Y., The Thermodynamics of Energy Conversions, Elsevier Direct Science, 2003. 2. Cengel, Y. A., Heat Transfer: A Practical Approach, McGraw-Hill, Inc., 1998. 3. Rifkin, J., Entropy, The Viking Press, 1980. 4. El-Wakil, M/ M., Power Plant Technology, McGraw-Hill, Inc., 1984. Periodicals 1. Energy and Buildings, Science Direct Elsevier Publishing Company. An international journal publishing articles about energy use in buildings and indoor environment quality. 2. Energy Conversion and Management, Science Direct Elsevier Publishing Company. This journal focuses on energy efficiency and management; heat pipes; space and terrestrial power systems; hydrogen production and storage; renewable energy; nuclear power; fuel cells and advanced batteries. 3. Energy and Buildings, Science Direct Elsevier Publishing Company, An international journal dedicated to investigations of energy use and efficiency in buildings. Government Agencies and Websites 1. How Things Work (http://howthingswork.virginia.edu). 2. How Stuff Works (http://www.howstuffworks.com). 3. California Energy Commission Consumer Energy Center (http://www.consumerenergycenter.org).