Energetics PDF by Dr Aditya Sharma Ghrera

ENERGETICS Thermodynamic terms, Mathematical form of first law, second law of thermodynamics, entropy, entropy change for a reversible process and irreversible process, entropy change for an isothermal expansion of an ideal gas, entropy of phase transitions and related numerical problems, Gibbs free...

ENERGETICS Thermodynamic terms, Mathematical form of first law, second law of thermodynamics, entropy, entropy change for a reversible process and irreversible process, entropy change for an isothermal expansion of an ideal gas, entropy of phase transitions and related numerical problems, Gibbs free energy and work function, Gibbs Helmholtz equation and Clausius and Clapeyron equation with their applications and related problems. By: Dr Aditya Sharma Ghrera  Energetics “the branch of science that deals with energy levels and the transfer of energy between systems and between different states of matter”  Important thermodynamic terms System The part of the universe selected for thermodynamic study is called system. For example boiling of water in a beaker. Surroundings The remaining part of the Universe around the system, which is not under study, is called surroundings. For example, boiling of water in a beaker is an example of system and everything else around the beaker is the surroundings.  Types of System Generally system may be classified into three categories: Open system: A system, which can exchange matter as well as energy with its surroundings, is called an open system. For example, boiling of water in an open beaker. Closed System: A system, which may exchange energy but not matter with surroundings, is called a closed system. For example, system remains inside the vessel. Isolated system: A system which can neither exchange matter nor energy with the surroundings is called an isolated system. There are no external forces at work in case of an isolated system. Homogeneous and Heterogeneous System Homogeneous system A system is said to be homogeneous if it is uniform throughout. Such type of system consists of only one phase. For example, a system containing only a pure solid or a pure liquid or a pure gas or completely miscible liquids or gases etc. Heterogeneous system A system is said to be heterogeneous if it is not uniform throughout. Such type of system consists more than one phase i.e.,Polyphase. For example, a system containing a mixture of two immiscible liquids or gases or solids etc.  Thermodynamic property A quantity which is either an attribute of an entire system or is a function of position which is continuous and does not vary rapidly over microscopic distances. Basic qualities used to define the condition of a substance, such as temperature, pressure, volume, concentration, surface tension, viscosity, enthalpy, and entropy.  Thermodynamic Properties Extensive property The properties, which depend on the amount of the material in the system, are called ‘Extensive properties’. For example, volume, internal energy, heat capacity, free energy, mass heat content, entropy, etc Intensive property The Properties, which do not depend (independent) on the amount of the material but depend upon the nature of the material in the system, are called intensive properties. For example, viscosity, surface tension, thermal conductivity, boiling point, freezing points, refractive index, Vapour pressure of as liquid, temperature, density, specific heat etc.  Thermodynamic Equilibrium Thermal Equilibrium: A system is said to be in thermal equilibrium if there is no flow of heat from one portion of the macroscopic system to the another portion. This is possible only if the temperature remains the same throughout in all parts of the system. Mechanical Equilibrium: A system is said to be in mechanical equilibrium if no mechanical work is done by one part of the macroscopic system to the another part of the system. This is possible only if the pressure remains constant throughout in all parts of the system. Chemical Equilibrium: A system is said to be in Chemical equilibrium if the composition of the various phases in the system does not change with time.  Thermodynamic Process It is the operation, which brings about the changes in the state or system. It is of the following types: Isothermal Process(dT=0) Adiabatic Process(dQ=0) Isobaric process(dP=0) Isochoric process(dV=0) Cyclic process(dE=0)  Path Reversible process: A process is said to be reversible if it is carried out infinitesimally slowly so that the driving force is only infinitesimally greater than the opposing force. Such types of processes are ideal and cannot be realized in practice. This is because a reversible process requires infinite time for its completion. Irreversible process: A process is said to be irreversible if it is not carried out infinitesimally slowly but the change is produced rapidly so that the system slowly does not remain in equilibrium condition.  LAWS OF THERMODYNAMICS Zeroth Law A B C If A & B and B & C are in thermal equil, then A and C are in thermal equil. [ie. At same T]  First Law Law of conservation of energy ❖ The first law of thermodynamics is simply an expression of the conservation of energy principle, and it asserts that energy is a thermodynamic property. ❖Energy can neither be created nor destroyed by any physical or chemical change. However, it can be changed into equivalent amount to the other form.  First Law (cont.) Energy can cross the boundary of a closed system in two distinct forms: heat and work. It is important to distinguish between these two forms of energy. Energy can be obtained from A primary source of energy When the energy obtained from a source is used in its original form, the source is said to be primary. An example is using the heat from a stove to boil water. A secondary source of energy When energy obtained is converted into another form before use, the energy source is said to be secondary. An example is using the heat from boiling water to turn a turbine; the heat is converted into rotary motion (mechanical energy or work).  First Law (cont.) We can use the principle of conservation of energy to define a function U called the internal energy. When a closed system undergoes a process by which it passes from state A to state B, if the only interaction with its surroundings is in the form of transfer of heat Q to the system, or performance of work W on the system, the change in U will be: ∆U = UB – UA = Q + W = Q + (– P ∆V).…………………..(1) If we had defined Q as heat librated by the system, Equation 1 would become ∆U = –Q + W = –Q + (– P ∆V) If we had defined W as work done by the system, Equation 1 would become ∆U = Q – W = Q – (+ P ∆V) The total energy of isolated system remains constant. For an isolated system there is no heat or work transferred with the surroundings, thus, by definition W = Q = 0 and therefore ∆U = 0. The first law of thermodynamics states that this energy difference ∆U depends only on the initial and final states, and not on the path followed between them. Both Q and W have many possible values, depending on exactly how the system passes from A to B, but Q + W = ∆U is invariable and independent of the path. If this were not true, it would be possible, by passing from A to B along one path and then returning from B to A along another, to obtain a net change in the energy of the closed system in contradiction to the principle of conservation of energy.  Limitation of the First Law Processes proceed in a certain direction and not in the reverse direction. The first law places no restriction on direction. A process will not occur unless it satisfies both the first and second laws of thermodynamics. Second law not only identifies the direction of process, it also asserts that energy has quality as well as quantity.  Second Law In any spontaneous process, there is always an increase in the entropy of the universe. From our definitions of system and surroundings: DSuniverse = DSsystem + DSsurroundings Three possibilities: – If DSuniv > 0…..process is spontaneous – If DSuniv < 0…..process is spontaneous in opposite direction. – If DSuniv = 0….equilibrium Here’s the catch: We need to know DS for both the system and surroundings to predict if a reaction will be spontaneous!  Second Law (cont.) Consider a reaction driven by heat flow from the surroundings at constant P Exothermic Process: DSsys = – heat/T = – Q/T DSsurr = heat/T = Q/T Endothermic Process: DSsys = heat/T = Q/T DSsurr = – heat/T = – Q/T  Entropy Change for Reversible and Irreversible process Reversible process Irreversible process DSuniverse = DSsystem + DSsurroundings DSuniverse = DSsystem+ DSsurroundings Reversible process proceed when Tsystem = T1 & Tsurrounding = T2 Tsystem ~ Tsurrounding If T2 > T1, heat will pass from surr to sys DSsystem = dQ DSsystem = dQ T T1 DSsurroundings = – dQ DSsurroundings = – dQ T T2 DSuniverse = 0 DSuniverse = dQ – dQ T1 T2 DSuniverse > 0  Third Law The entropy of a perfect crystal at 0K (absolute zero temperature) is zero The third law provides the reference state for use in calculating absolute entropies.  Molar Heat Capacity Amount of heat required to raise the temperature of 1 mole of substance (of system) by 1 °C. C = dQ / dT At constant Volume At constant Pressure From 1st Law of thermodynamics From the relation between enthalpy and ‘U’ dE = dQ ‒ PdV dH = dE + d(PV) If heat is added at constant volume, then the second term of this relation vanishes dH = dQ + VdP dE = dQ If heat is added at constant pressure, then the second term of this relation vanishes C = dE /dT dH = dQ Prove: CP – CV = R nCP dT = dH nCV dT = dE nCP dT ‒ nCV dT = dH ‒ dE n(CP ‒ CV) dT = dE + d(PV) ‒ dE n(CP ‒ CV) dT = d(PV) n(CP ‒ CV) dT = d(nRT) n(CP ‒ CV) dT = nR dT (CP ‒ CV) = R ENTROPY CHANGE FOR AN IDEAL GAS From the first law of thermodynamics dE= dQ + dW -------- 1 Since dS= dQ/T (2nd Law of thermodynamics) dQ=TdS dW= – PdV Putting the value of dQ and dW in equation 1 We get :- dE= TdS – PdV -------- 2 Volume)  7 HENCE DERIVED  ENTROPY CHANGE FOR AN IDEAL GAS For Isochoric Process……… Vf = Vi From eq 4: dS = n CV ln Tf /Ti For Isobaric Process……… Pf = Pi From eq 7: dS = n CP ln Tf /Ti For Isothermal Process……… Tf = Ti From eq 4 and 7: dS = n R ln Vf /Vi = nR ln Pi /Pf ENTROPY CHANGE FOR PHASE TRANSITION Since, at constant pressure: ΔH = ΔQP Entropy change of fusion……… Solid = Liquid ΔSfusion = ΔHfusion / Tmelting Entropy change of vaporization…… Liquid = Gas ΔSvaporization = ΔHvaporization / Tboiling Entropy change of sublimation……… Solid = Gas ΔSsublimation = ΔHsublimation / Tsublimation Entropy change of allotropes……… A = B ΔStransition = ΔHtransition / Ttransition FREE ENERGY AND WORK FUNCTION All spontaneous process have a tendency to achieve a state of minimum energy and maximum entropy. But in actual practice it is not possible to achieve both, minimum energy and maximum entropy. Many endothermic process, like evaporation, are spontaneous. Some athermal process (ΔH=0) are spontaneous. Here entropy overweigh enthalpy or free energy factor. Some spontaneous process proceed with a decrease in entropy. H2 and O2 gases produces liquid water. Functions introduced to decide feasibility of a process: Helmholtz free energy function OR Work function ‘A’ Gibbs free energy function OR thermodynamic potential ‘G’  A = E – TS G = H – TS ΔA = ΔE – T ΔS – S ΔT ΔG = ΔH – T ΔS – S ΔT at constant temperature since, ΔH = ΔE + PΔV + VΔP ΔA = ΔE – T ΔS ΔG = ΔE + PΔV + VΔP – T ΔS – SΔT for a reversible process at constant temp and pressure ΔS = Qrev / T ΔG = ΔE + PΔV – T ΔS ΔA = ΔE – Qrev for a reversible process also, ΔE = Qrev + Wrev ΔS = Qrev / T and ΔA = Qrev + Wrev – Qrev ΔE = Qrev + Wrev ΔA = Wrev So, ΔG = Qrev + Wrev + VΔP – Qrev If work is done by system ΔG = Wrev + PΔV ΔA = – Wrev  GIBB’S-HELMHOTLZ EQUATION IN TERMS OF GIBB’S FREE ENERGY It is the equation which relates Gibb’s free energy to different temperatures. It can be derived as follows: G = H − TS dG = dH − TdS − SdT dG = d ( E + PV ) − TdS − SdT dG = TdS − PdV − TdS − SdT + VdP + PdV dG = VdP − SdT  d G p = − Sp dT This equation relate different change in d G1 = − S1 dT Gibbs free energy with d G 2 = − S2 dT respect to Subtracting equations temperature. d (G 2 − G1) = −( S 2 − S 1) dT If two different dDG temperature and = − DS dT corresponding Gibbs dDG DS = − free energy is given dT DG = DH − TDS then we calculate dDG enthalpy of system. DG = DH + T ( ) dT  GIBB’S-HELMHOTLZ EQUATION IN TERMS OF FREE ENERGY / WORK FUNCTION A= E – TS Differentiating both sides dA= dE – T dS – S dT dA = (T dS – P d V) – T dS – S dT dA = P dV - S dT At Constant Volume PdV = 0 dA V = – S dT dA1 = – S1 dT dA2 = – S2 dT Subtracting above equations d(A2 – A1) = –(S2 – S1)dT d DA = – DSdT DS = – (d DA)V (dT) DA = DE – T DS Substituting the value of DS in above equation DA = DE + T (d DA) (dT) - GIBBS HELMHOLTZ EQN  APPLICATION OF GIBBS HELMHOLTZ EQUATION To determine the relationship between enthalpy and electrode potential ΔG = − nFE  d( − nFE)  − nFE = ΔH + T    dT   dE  − nFE = ΔH − nFT    dT   dE  ΔH = − nFE + nFT    dT    dE   ΔH = − nF  E − T     dT    CLAUSIUS-CLEYPRON EQUATION A thermodynamic relation between change of pressure with change of temperature of a system at equilibrium G = H – TS dG = VdP – SdT dGA = VA dP – SA dT dGB = VB dP – SB dT For an equilibrium transition of one mole of a substance from phase A to phase B at constant pressure: ΔG = 0 ----------- 1 GB – GA = 0 GB = GA ----------- 2 GB + dGB = GA + dGA -------------- 3 dGB = dGA --------------- 4 VB dP – SB dT = VA dP – SA dT ( VB – VA ) dP = ( SB – SA ) dT V dP = S dT dP / dT = S/ V dP / dT = H / T V ----------------- CLAUSIUS CLAPEYRON EQUATION.  CONDITION OF INTEGRATION Volume of product/reactant ˃˃ Volume of reactant/product H2 O (l) → H2 O (g) dP / dT = ∆Hvap / T( Vg –Vl ) Vg ˃ ˃ Vl dP / dT = ∆Hvap / T Vg For an ideal gas: Vg = RT/P dP / dT = ∆Hvap P / T. RT  FOR SPECIFIC CASES 1. H2 O (s) → H2 O (l) dP / dT = HF / T ( Vl – Vs ) ----------- ( particular phase fusion ) 2. H2 O (l) → H2 O (g) dP / dT = Hvap / T( Vg –Vl ) dP / dT = ∆Hvap P / T Vg dP / dT = ∆Hvap P / RT2 dP/P = ∆Hvap dT/RT2 dP/P = ∆Hvap ( dT/RT2) ln (P2 / P1) = ∆Hvap (1/T1 - 1/T2)/R APPLICATIONS