MSE 3050, Phase Diagrams and Kinetics, Leonid ZhigileiReview of classical thermodynamicsFundamental Laws, Properties and Processes (2)Entropy and the Second LawConcepts of equilibrium Reversible and irreversible processes The direction of spontaneous change Entropy and spontaneous/irreversible processesCalculation of entropy in isochoric and isobaric processesCalculation of entropy in reversible and irreversible processesReading: Chapters 3.1 – 3.5, 3.14 – 3.17 of Gaskellor the same material in any other textbook on thermodynamicsMSE 3050, Phase Diagrams and Kinetics, Leonid Zhigilei2ndLaw of ThermodynamicsA system left to itself will either1. Remains in the same state indefinitely (system is in equilibrium). The system will move from the equilibrium state only if acted on by some external impact.2. Will move, of its own accord, to some other state. The system in this case is in a non-equilibrium state and will move towards equilibrium state in a natural or spontaneousprocess.Spontaneous transition from non-equilibrium state to the equilibrium state cannot be reversed without application of an external force – it is an irreversible process.Examples of spontaneous/irreversible processes:Mixing of different gasesHeat flow from hot to cold objectsT1< T2T1= T2Spontaneous processes are not necessarily instantaneous processes – kinetics!MSE 3050, Phase Diagrams and Kinetics, Leonid ZhigileiHow to predict which process will proceed spontaneously?1stlaw: U and H are state functions - if the system is going from A to B, ΔU(A→B) = -ΔU(B→A) or ΔH(A→B) = -ΔH(B→A)But fist law does not tell us which reaction, forward or reverse is natural or spontaneous one.Intuition:The energetic driving force- the tendency tofall to a lower potential energy, e.g. releaseheat in a reaction.Indeed, often spontaneous changes are exothermic (reaction produces heat), e.g. H2(gas) + ½ O2(gas) → H2O (liquid) ΔH = -286 kJmol-1But, reactions can also occur spontaneously which are endothermic, e.g. H2O (liquid,105°C) → H2O (gas,105°C) ΔH = +44 kJmol-1A negative sign of ΔH favors but does not guarantee spontaneity.ΔHABMSE 3050, Phase Diagrams and Kinetics, Leonid ZhigileiQuantification of irreversibilityIt is desirable to find some common measure of the tendency of asystem to change spontaneously. This measure should be¾ A thermodynamic property (state function).¾ It should change in a characteristic manner (e.g. always increase) when a process proceeds spontaneously.Such function, entropy (from τροπη - transformation in Greek), has been introduced by Clausius in 1850.Second Law of Thermodynamics can be formulated in different ways. One possible formulation is: There exist a state function, the entropy S, which for all reversible processes is defined by dS = δqrev/Tand for all irreversible processes is such that dS > δq/Tor in general, dS ≥ δq/TEntropy is a state function whose change is defined for a reversible process at T where Q is the heat absorbed: ΔS = Q/TFor an isolated system δq = 0 ⇒ dS ≥ 0. Entropy is maximized in any spontaneous process. This will be the basis for definition of the equilibrium conditions.MSE 3050, Phase Diagrams and Kinetics, Leonid ZhigileiWhy q/T ?For qualitative understanding of why the quantity q/T is used as a measure of the degree of irreversibility let’s consider an example from Gaskell, §3.3.Let’s consider two irreversible processes:1. Conversion of work to heat2. Flow of heat down a T gradientThree processes with different degree of irreversibility:e = c + ddcT2T2T1qqqT1T2T2> T1qq/T2< q/T1All three processes are irreversible. The e is just a sum of cand d: should be the most irreversible. Both heat production and temperatures are important in defining a scale of irreversibility.c is lessirreversible than eMSE 3050, Phase Diagrams and Kinetics, Leonid ZhigileiSummary on Entropy¾ Entropy is a state function.¾ When the weight-heat reservoir system, discussed above, undergoes a spontaneous process which causes the adsorption of heat q at a constant temperature T, the entropy produced by the system ΔS = q/T. The increase in entropy, caused by the process, is thus a measure of the degree of irreversibility. Thus, S is not conserved.¾ The increase in entropy due to the occurrence of an irreversible process arises from the degradation of energy potentially available for useful work into heat. ¾ In a reversible process (the driving force is infinitesimal and the process proceeds at an infinitesimal rate) the system moves through a continuum of equilibrium states and the entropy is not created, it can only be transferred from one part of the system to another. For more on entropy in reversible processes see Gaskell, §3.4 – 3.9.¾ The entropy of an adiabatic system cannot decrease. It increases in an irreversible process and remains constant during a reversible process.S of an open system can decrease at the expense of entropy increase of another system (environment)systemsystemenvironmentenvironmentδQ0syso envttdS dS dS=+≥MSE 3050, Phase Diagrams and Kinetics, Leonid ZhigileiThe Second Law AgainWe can reformulate the second law in the following way:For every thermodynamic system there exist an extensive state function called entropy which can be calculated by a reversible path from an arbitrary chosen reference state by integrating the heat absorbed by the system divided by the absolute temperature.The entropy of a system plus its surroundings (together forming “the universe” – an isolated system) never decreasesand increases in any irreversible process.The 3rdlaw of thermodynamics:The third law of thermodynamics, states that if one could reach absolute zero temperature (all the thermal motion of atoms couldbe removed) and a complete internal equilibrium, all bodies would have the same entropy. In other words, a body at absolute zero could exist in only one possible state, which would possessa definite energy, called the zero-point energy. This state is defined as having zero entropy. The 3rdlaw has been first formulated by Walter Nernst and also known as the Nernst heat theorem.The 3rdlaw allows us to define absolute values of entropy at a given T:dTTcSST0P0T∫+=dTTcTqdST0PT0rev∫∫==δthus where S0= 0MSE 3050, Phase Diagrams and Kinetics, Leonid ZhigileiCombined statement of the 1stand 2ndlawsFor a closed system and a reversible processdU = δq-δw, δq = TdS, and, assuming that work