Entropy (YAC- Ch. 6)Entropy – A PropertyEntropy (cont’d)Increase of Entropy Principle (YAC- Ch. 6-3)Second Law & Entropy Balance (YAC- Ch. 6-4)Entropy Generation ExampleEntropy (YAC- Ch. 6)•Introduce the thermodynamic property called Entropy (S) • Entropy is defined using the Clausius inequality•Introduce the Increase of Entropy Principle which states that–the entropy for an isolated system (or a system plus its surroundings) is always increases or, at best, remains the same.–Second Law in terms of Entropy•Learn to use the Entropy balance equation: entropy change = entropy transfer + entropy change. •Analyze entropy changes in thermodynamic process and learn how to use thermodynamic tables •Examine entropy relationships (Tds relations), entropy relations for ideal gases.•Property diagrams involving entropy (T-s and h-s diagrams)In this Chapter, we will: Entrpy.ppt, 10/18/01 pagesEntropy – A Property• Entropy is a thermodynamic property; it can be viewed as a measure of disorder. i.e. More disorganized a system the higher its entropy.• Defined using Clausius inequality where Q is the differential heat transfer & T is the absolutetemperature at the boundary where the heat transfer occurs• Clausius inequality is valid for all cycles, reversible and irreversible.• Consider a reversible Carnot cycle:th, from Carnot efficiceny 1 1 ,Q QTherefore, 0 for a reversible Carnot cycle 0T TH L L L L LH L H H H HrevQ Q Q Q T Q TT T T Q T Q T            �� �• Since , i.e. it does not change if you return to the same state, it must be a property, by defintion:• Let’s define a thermodynamic property entropy (S), such that2 22 11 1, for any reversible process dSThe change of entropy can be defined based on a reversible processrev revQ QdS S ST T     0revTQ0revTQTrue for a Reversible Process onlyEntropy (cont’d) Since entropy is a thermodynamic property, it has fixed values at a fixed thermodynamic states. Hence, the change, S, is determined by the initial and final state. BUT..The change is = only for a Reversible Process12reversibleprocessanyprocessTS2 11 22 2 22 11 1 12 12 11 20From entropy definitionQ QdS= , 0Therefore, revrev rev revrevrevQ Q QT T TQ QdST T T TQ QdS S S ST TQS S ST                                                                   �� �21, This is valid for all processesQ Q, since = ,T Trev irrevQdS dS dST            TQConsider a cycle, whereProcess 2-1 is reversible and 1-2 may or may not be reversibleIncrease of Entropy Principle (YAC- Ch. 6-3)Implications:•Entropy, unlike energy, is non-conservative since it is always increasing. •The entropy of the universe is continuously increasing, in other words, it is becoming disorganized and is approaching chaotic.• The entropy generation is due to the presence 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.• The above is another statement of the second lawEntropy changeEntropy Transfer(due to heat transfer)Entropy GenerationThe principle states that for an isolated Or a closed adiabatic Or System + SurroundingsA process can only take place such that Sgen 0 where Sge = 0 for a reversible process onlyAnd Sge can never be les than zero.Increase of Entropy PrincipleSecond Law & Entropy Balance (YAC- Ch. 6-4)• Increase of Entropy Principle is another way of stating the Second Law of Thermodynamics:Second Law : Entropy can be created but NOT destroyed (In contrast, the first law states: Energy is always conserved) •Note that this does not mean that the entropy of a system cannot be reduced, it can.• However, total entropy of a system + surroundings cannot be reduced • Entropy Balance is used to determine the Change in entropy of a system as follows: Entropy change = Entropy Transfer + Entropy Generation where,Entropy change = S = S2 - S1Entropy Transfer = Transfer due to Heat (Q/T) + Entropy flow due to mass flow (misi – mese)Entropy Generation = Sgen 0 For a Closed System: S2 - S1 = Qk /Tk + SgenIn Rate Form: dS/dt = Qk /Tk + SgenFor an Open System (Control Volume):Similar to energy and mass conservation, the entropy balance equations can be simplifiedUnder appropriate conditions, e.g. steady state, adiabatic….CVgeneeiikkcvSsmsmTQdtdS,Entropy Generation ExampleShow that heat can not be transferred 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