Advanced Thermodynamics: Lecture 5 Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
Heat engines They receive heat from a high-temperature source (solar energy, oil furnace, nuclear reactor, etc.). They convert part of this heat to work (usually in the form of a rotating shaft). They reject the remaining waste heat to a low-temperature sink (the atmosphere, rivers, etc.). They operate on a cycle. Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
Heat engines High-temperature SOURCE Q in HEAT ENGINE W net,out Q out Low-temperature SINK Image source: Thermodynamics An Engineering Approach, Cengel and Boles, 7th edition Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
Schematic of a Power Plant Energy source (such as a furnace) System boundary Q in Boiler W out W in Pump Turbine Condenser Q out Energy sink (such as the atmosphere) FIGURE 6–10 Total work output �� W net , out = W out − W in Image source: Thermodynamics An Engineering Approach, Cengel and Boles, 7th edition Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661 ��
Thermal Efficiency Defined as Thermal Efficiency = Net work output Total heat input Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
Thermal Efficiency Defined as Thermal Efficiency = Net work output Total heat input η th = W net , out Q h Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
Thermal Efficiency Defined as Thermal Efficiency = Net work output Total heat input η th = W net , out Q h Since W net , out = Q H − Q L Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
Thermal Efficiency Defined as Thermal Efficiency = Net work output Total heat input η th = W net , out Q h Since W net , out = Q H − Q L η th = 1 − Q L Q H Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
Second Law: Kelvin Planck Statement It is impossible for any device that operates on a cycle to receive heat from a single reservoir and produce a net amount of work. Thermal energy reservoir · Q H = 100 kW · W net,out = 100 kW HEAT ENGINE · Q L = 0 Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
Second Law: Kelvin Planck Statement It is impossible for any device that operates on a cycle to receive heat from a single reservoir and produce a net amount of work. Thermal energy reservoir · Q H = 100 kW · W net,out = 100 kW HEAT ENGINE · Q L = 0 In other words No heat engine can have a thermal efficiency of 100 percent, or as for a power plant to operate, the working fluid must exchange heat with the environment as well as the furnace. Image source: Thermodynamics An Engineering Approach, Cengel and Boles, 7th edition Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
Refrigeration and heat pumps Surrounding medium such as the kitchen air Q H CONDENSER 800 kPa 800 kPa 30 ° C 60 ° C W net,in EXPANSION COMPRESSOR VALVE 120 kPa 120 kPa –25 ° C –20 ° C EVAPORATOR Q L Refrigerated space Image source: Thermodynamics An Engineering Approach, Cengel and Boles, 7th edition Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661 ��
Refrigeration schematic Warm environment at T H > T L Required Q H input W net,in R Desired output Q L Cold refrigerated space at T L Image source: Thermodynamics An Engineering Approach, Cengel and Boles, 7th edition Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661 ��
Coefficient of performance: Refrigeration Defined as COP R = Desired output Q L Required input = W net , in Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
Coefficient of performance: Refrigeration Defined as COP R = Desired output Q L Required input = W net , in Since W net , in = Q H − Q L Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
Coefficient of performance: Refrigeration Defined as COP R = Desired output Q L Required input = W net , in Since W net , in = Q H − Q L Q L 1 COP R = = Q H Q H − Q L Q L − 1 Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
Heat Pump schematic Warm heated space at T H > T L Desired output Q H W net,in HP Required input Q L Cold environment at T L Image source: Thermodynamics An Engineering Approach, Cengel and Boles, 7th edition Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
Coefficient of performance: Heat Pump Defined as COP HP = Desired output Q H Required input = W net , in Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
Coefficient of performance: Heat Pump Defined as COP HP = Desired output Q H Required input = W net , in Since W net , in = Q H − Q L Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
Coefficient of performance: Heat Pump Defined as COP HP = Desired output Q H Required input = W net , in Since W net , in = Q H − Q L Q H 1 COP HP = = 1 − Q L Q H − Q L Q H Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
Coefficient of performance: Heat Pump Defined as COP HP = Desired output Q H Required input = W net , in Since W net , in = Q H − Q L Q H 1 COP HP = = 1 − Q L Q H − Q L Q H COP HP = COP R + 1 Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
Second Law: Clausius Statement It is impossible to construct a device that operates in a cycle and produces no effect other than the transfer of heat from a lower-temperature body to a higher-temperature body. Warm environment Q H = 5 kJ W net,in = 0 R Q L = 5 kJ Cold refrigerated space Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
Second Law: Clausius Statement It is impossible to construct a device that operates in a cycle and produces no effect other than the transfer of heat from a lower-temperature body to a higher-temperature body. Warm environment Q H = 5 kJ W net,in = 0 R Q L = 5 kJ Cold refrigerated space Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
Equivalence of Kelvin–Planck and Clausius Statements High-temperature reservoir at T H Q H Q H + Q L HEAT W net REFRIG- ENGINE ERATOR η th = 100% = Q H Q L Low-temperature reservoir at T L ( a ) A refrigerator that is powered by Image source: Thermodynamics An Engineering Approach, Cengel and Boles, 7th edition Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
Equivalence of Kelvin–Planck and Clausius Statements High-temperature reservoir at T H Q L REFRIG- ERATOR Q L Low-temperature reservoir at T L ( b ) The equivalent refrigerator Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661 Image source: Thermodynamics An Engineering Approach, Cengel and Boles, 7th edition
Heat Rejection by a Refrigerator The food compartment of a refrigerator is maintained at 4C by removing heat from it at a rate of 360 kJ/min. If the required power input to the refrigerator is 2 kW, determine (a) the coefficient of performance of the refrigerator and (b) the rate of heat rejection to the room that houses the refrigerator. Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
Heating a House by a Heat Pump A heat pump is used to meet the heating requirements of a house and maintain it at 20C. On a day when the outdoor air temperature drops to -2C, the house is estimated to lose heat at a rate of 80,000 kJ/h. If the heat pump under these conditions has a COP of 2.5, determine (a) the power consumed by the heat pump and (b) the rate at which heat is absorbed from the cold outdoor air. Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
Internally and Externally Reversible Processes A process is called internally reversible if no irreversibilities occur within the boundaries of the system during the process. Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
Internally and Externally Reversible Processes A process is called internally reversible if no irreversibilities occur within the boundaries of the system during the process. A process is called externally reversible if no irreversibilities occur out- side the system boundaries during the process. Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
Internally and Externally Reversible Processes A process is called internally reversible if no irreversibilities occur within the boundaries of the system during the process. A process is called externally reversible if no irreversibilities occur out- side the system boundaries during the process. A process is called totally reversible , or simply reversible, if it involves no irreversibilities within the system or its surroundings. Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
Internally and Externally Reversible Processes A process is called internally reversible if no irreversibilities occur within the boundaries of the system during the process. A process is called externally reversible if no irreversibilities occur out- side the system boundaries during the process. A process is called totally reversible , or simply reversible, if it involves no irreversibilities within the system or its surroundings. A totally reversible process involves no heat transfer through a finite temperature difference, no non–quasi-equilibrium changes, and no friction or other dissipative effects. Shivasubramanian Gopalakrishnan sgopalak@iitb.ac.in ME 661
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