This Class 2nd & 3rd Law of Thermodynamics: (Directionality /Spontaneity, Scale) Initialization Q1=100 Non-EQ Q2=50 T1=10 T2=1 Q1/T1=10 < Q2/T2=50 W=50 Q1=100 Non-EQ Q2=20 T1=10 T2=1 Q1/T1=10 < Q2/T2=20 W=80 Q1=100 EQ Q2=10 T1=10 T2=1 Q1/T1=10 = Q2/T2=10 W=90 Carnot Cycle A Temperature Scale System A at T Q System B at T-1 Same Mechanical Effect Irrespective of Material Properties Carnot Engine in Details (Assignment – Self Reading) All steps are reversible, so maximum work is expected => Incorporation of Idealism Continuing….. As General Case Here, πΆπ. ln π‘1 π‘2 + π . ln π3 π2 = 0 & πΆπ. ln π‘2 π‘1 + π . ln π1 π4 =0 In Carnot cycle T1 & T2 are fixed => V2/V1 =V3/V4 Entropy: One of Most Used Terms Continuing with Entropy Both Statements (Clausius & Kelvin) & More…. Clausius: It is not possible to draw a certain amount of heat, say Q, from a cold body and transfer it all to a hot body. Kelvin: It is not possible to convert heat entirely into work. Hot Q2 Hot Hot 1 1 3 2 Q1-Q2 W=Q1-Q2 Q2 Q2 Q2 Cold Q1-Q2 Q1 Q2 Cold Cold Better Than Reversible Efficiency: Possible or not? Hot Q=100 Q=10 W=90 Reversible Engine Better Than Reversible Engine Q=9 Q=100 W1 – W = 1 => This way we can generate work for ever => Impossible Demand (Reversible path is already in maximum ordered energy path out of total energy) W1=91 Cold W Qs From source Qloss To sink Uncompensated Transformation (Qs-Qloss)rev > (Qs-Qloss)irre Qloss (heat loss) is min. for reversibility dS is the difference between heats in transit i.e. transfer and loss. Entropy Change for an Isothermal Expansion of an Ideal Gas Entropy: Extensive Property Molar Entropy (Entropy per Mole): Intensive Property Exothermic Reactions: Entropy Change for Surroundings For an adiabatic reversible change: βSsys = 0 and βSsurr = 0 Some Essential Derivations Entropy Balance S • Having directional property of a process • Guided by a fundamental law (entropy can’t decrease: Which Law??) • Definable non-zero generation term of a process • Universally applicable state variable with physical significance • Another balance equation (more access to a system) Basic Ideas Reversible Process Irreversible Process Basic Ideas A Matter Exchange in the system + Irreversibility Cyclic Process Systems in Non-equilibrium Basic Ideas Expression Rate of Entropy Generation = Net change of entropy flow due to flows of mass in and out of the system + Net change of entropy flow due to flow of heat across the system boundary + Rate of internal generation of entropy within the system Entropy Generation = 0 Entropy Generation > 0 => at equilibrium => All non-equilibrium conditions Entropy Balance Equation for Open System Important Equation Continuing A One Problem Another Problem Continuing with the Solution Continuing with the Solution Statements of Second Law For Irreversible Process Overall Entropy Increases: Prove Mathematically: Assignment Few Important Points A Problem Continuing….. Problem (from different Universities) Another Problem Third Law: Relooking The Definition 1. If a single process of reversible extraction of heat results in the reduction of the temp. for a crystal to the lowest measurable temp. near 0K, then zero entropy at 0K remains an obvious extrapolation from that measured point. 2. What the 3rd law tells us in real life is that curves of many reasonable physical quantities plotted against T must come in flat as T approaches 0. Kittel-Kroemer 3. The entropy of a system at absolute 0 is a universal constant, which may be taken to be 0. Huang 4. The entropy of a system approaches a constant value as the temperature approaches zero. Molten SiO2 to Glass Different S0 for same matter: Not Permissible Attaining T=0: Infinite Reversible Cycles Third Law: Relooking The Definition A Third Law: Relooking The Definition Third Law & Beginning of Statistical Journey Continuing….. Few Points 2nd law: The entropy of an isolated system never decreases. liquid S supercooled liquid glass residual entropy crystal T −1 ο¦ οΆ S (U ,V , N ,...) οΆ ο·ο· T οΊ ο§ο§ οΆU ο¨ οΈV , N Sample Problems (Assignments) 1. Derive the Relation 2. Drive the Relations 3. Follow any standard text books (preferably references) to see the solved problems related to 2nd as well as 3rd Laws of thermodynamics and practice the derivations 4. Answer: 5. Entropy & Information Picking Red Ball Ball Picking Red with => with Certainty Certainty => Knowledge => Precise Information toDecreasing Definefrom left the to right, while System => entropy is Decreasing from left increasing to right, while entropy is increasing https://www.youtube.com/watch?v=9r7FIXEAGvs Entropy & Information-2 1 Entropy & Information-3 Picking ‘A’ with Certainty => Precise Information to Define the System => Decreasing from left to right, while entropy is increasing Entropy & Information-4 A Entropy & Information-5 A Next Class Quick Review – III Some Concepts, Definitions & Aspects