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Note for Basics of Mechanical Engineering - BME by Yash Yadav

  • Basics of Mechanical Engineering - BME
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www.vidyarthiplus.com Chapter 4 THE SECOND LAW OF THERMODYNAMICS 4.1 Limitations of First Law of Thermodynamics If a well insulated tank of fluid is stirred by a rotating paddle wheel, the energy of the fluid increases. If the stirrer is stopped, however the energy of the fluid will not decrease and cause the stirrer to rotate in the opposite direction. The possibility of this process proceeding in the opposite direction is not excluded by the first law of Thermodynamics. Hence first law of thermodynamics does not allow us to predict whether a proposed conceived energy conversion is possible or not. In all the internal combustion engines fuel and air mixture is supplied at room temperature. This mixture undergoes combustion inside the engine and gives out work. Exhaust gases coming out of the engine are always at higher temperature, indicating that some heat is taken away into atmosphere. Hence, in all the IC engines only a part of the heat is converted into work. From our experience we know that if any attempt is made to convert all the heat into work, our effort will go in vain. This limitation in the extent of energy conversion has also not been addressed in first law of thermodynamics. 4.2 The Second law of Thermodynamics Kelvin Planck’s statement : It is impossible to construct a device that, operating continuously, will produce no effect other than transfer of heat from a single thermal reservoir and performance of an equal amount of work. The term thermal reservoir refers to a very large system in stable equilibrium, to which or from which, any amount of heat can be transferred at constant temperature. A thermal reservoir supplying heat continuously at constant temperature is known as source. (Example : Sun) A thermal reservoir receiving heat continuously at constant temperature is known as sink. (Examples : River, Sea) From Kelvin-Planck statement it is clear that for any system to operate in a cycle and to give out work continuously it should interact with a minimum of two reservoirs at different temperatures. The system will receive heat from the high temperature reservoir and reject heat to the low temperature reservoir. Such devices are known as heat engines. Performance (or) Efficiency of a heat engine can be expressed as the ratio of desired output to the required input. In a heat engine the desired output is net work output and the required input is total heat input 42 www.vidyarthiplus.com

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www.vidyarthiplus.com Source Desired Effect Qin Heat Engine W Required Effect Qout Sink Figure 4.1 Heat Engine η= Wnet Qin ...(4.1) From first law of thermodynamics ΣQ = ΣW Qin − Qout = Wnet ...(4.2) Clausius statement : Unaided by an external agency heat can not be transferred from a body at lower temperature to a body at higher temperature. Devices that are used to transfer heat from a body at lower temperature to a body at higher temperature are known as refrigerators (or) heat pumps. If the high temperature side is atmosphere it is a refrigerator. If the low temperature side is atmosphere it is known as a heat pump. The performance index here is called coefficient of performance (COP). In refrigerator (and heat pumps) the performance is the ratio of two independent parameters and hence the possibility of getting the value more than unity is always there. But the term efficiency is restricted to a maximum of unity. Hence the term efficiency is not used here. COP = Desired Effect Re quired Effect COP = Q2 W 43 www.vidyarthiplus.com

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www.vidyarthiplus.com Taking work as external agency, for refrigerators (Figure 4.2) ...(4.3) From first law ΣQ = ΣW Q1 − Q2 = W COP = Q2 Q1 − Q2 Sink [Atmosphere] Required Effect Q1 Refrige rator W Desired Effect Q2 Source [conditioned Space] Figure 4.2 Refrigerator 44 www.vidyarthiplus.com

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www.vidyarthiplus.com Sink [Conditioned Space] Desired Effect Q1 Heat Pump W Required Effect Q2 Source [Atmosphere] Figure 4.3 Heat Pump Similarly for a heat pumps (Figure 4.3) COP = Desired Effect Re quired Effect Q1 W Since, Q1 + Q2 = W COP = COP = ...(4.4) Q1 Q1 − Q2 ...(4.5) 45 www.vidyarthiplus.com

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