Objectives• Introduce the thermodynamic property entropy (S) using the Clausius inequality• Recognize the fact that the entropy is always increasing for an isolated system (or a system plus its surroundings) based on the increase of entropy principle• Analysis of entopy change of a thermodynamic process (how to use thermodynamic table, ideal gas relation)• Property diagrams involving entropy (T-s and h-s diagrams)• Entropy balance: entropy change = entropy transfer + entropy changeEntropy• Entropy: a thermodynamic property, can be used as a measure of disorder. The more disorganized a system the higher the entropy.• Defined using Clausius inequality 0QTδ≤∫!• This inequality is valid for all cycles, reversible and irreversible.• Consider a reversible Carnot cycleth, from Carnot efficiceny 1 1 ,QQTherefore, 0 for a reversible Carnot cycle 0TTHL L LLLHL H HHHrevQQ Q Q T Q TTTT Q TQTδηδδ= − =− =− ===∫∫∫!!!• Define a thermodynamic property entropy (S), such that222111, for any reversible process dSThe change of entropy can be defined based on a reversible processrev revQQdS S STTδδ===−∫∫Entropy-2• Since entropy is a thermodynamic property, it has fixed values at a fixed thermodynamic states.12reversibleprocessanyprocessTS211222 22111 12121120From entropy definitionQQdS= , 0Therefore, revrev rev revrevrevQQ QTT TQQdSTTTTQQdS S S STTQSS STδδ δδδδδδδδ=+ ≤ == = + ≤==−=∆∆= − ≥∫∫ ∫∫∫ ∫ ∫∫∫ ∫!!!21, This is valid for all processesQQ, since = ,TTrev irrevQdS dS dSTδδδ ≥> ∫• The entropy change during an irreversible process is greater than the integral of δQ/T during the process. If the process is reversible, then the entropy change is equal to the integral of δQ/T. For the same entropy change, the heat transfer for a reversible process is less than that of an irreversible. Why?Entropy Increase Principle221 gen1222111, define entropy generation Swhere 0. If the system is isolated and "no" heat transferThe entropy will still increase or stay system gengenQSS STQQSSS STTSδδδ∆= − ≥ ∆=−= +≥ ≥∫∫∫the same but never decrease0, entropy increase principlesystem genSS∆=≥• A process can take place only in the direction that complies with the increase of entropy principle, that is, Sgen≥0.• Entropy is non-conservative since it is always increasing. The entropy of the universe is continuously increasing, in other words, it is more disorganized and is approaching chaotic.• The entropy generation is due to the existence of irreversibilities. Therefore, the higher the entropy generation the higher the irreversibilities and, accordingly, the lower the efficiency of a device since a reversible system is the most efficient system.Entropy Generation ExampleExample: Show that the heat can not transfer from the low-temperature sink to the high-temperature source based on the increase of entropy principle.Source800 KSink500 KQ=2000 kJ∆S(source) = 2000/800 = 2.5 (kJ/K)∆S(sink) = -2000/500 = -4 (kJ/K)Sgen= ∆S(source)+ ∆S(sink) = -1.5(kJ/K) < 0It is impossible based on the entropy increase principleSgen≥0, therefore, the heat can not transfer from low-temp. to high-temp. without external work input• If the process is reversed, 2000 kJ of heat is transferred from the source to the sink, Sgen=1.5 (kJ/K) > 0, and the process can occur according to the second law• If the sink temperature is increased to 700 K, how about the entropy generation? ∆S(source) = -2000/800 = -2.5(kJ/K)∆S(sink) = 2000/700 = 2.86 (kJ/K)Sgen= ∆S(source)+ ∆S(sink) = 0.36 (kJ/K) < 1.5 (kJ/K)Entropy generation is less than when the sink temperature is 500 K, less irreversibility. Heat transfer between objects having large temperature difference generates higher degree of
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