THERMODYNAMICS

1. THERMODYNAMICS • The branch of science which deals with the study of different forms of energy and their interconversion is called thermodynamics.

2. System & Surroundings System Surroundings • A specified part of the universe which is under observation is called system. surroundings • The remaining portion of the universe which is not a part of the system is called surroundings. System

3. Types of System:

4. Open, closed and isolated system All physical and chemical processes taking place in open in our daily life are open systems because these are continuously exchanging mass and energy with the surroundings. Surroundings Matter System Matter Energy Matter Energy Energy

5. The state of the system & State Variable • State function: Those properties which determines a particular system is called state function. • Path function: Path function depends on the path of change from initial state to final state. • State function: The measureable properties required to describe the state of the system are called state variables.

6. Internal energy and internal energy change

7. Internal energy as a state function In thermodynamics internal energy(U) of the system may change , when Heat passes into or out of the system Work is done on or by the system Matter enters or leave the system • 1. Heat(Q): energy is exchanged between the system and the surroundings as heat if they are at different temperatures. ∆U = q • 2. Work(w): It is also a mode of transference between system & surroundings. Work done by the system on the surroundings is given by p∆V

8. Sign conventions • Work : a) positive , if work is done on the system. b) negative, if work is done by the system. • Heat : a) positive , if heat absorbed by the system. b) negative , if heat released by the system.

9. Types of changes Isothermal change: A change in which the temperature of the system remains constant.(∆T= 0) Adiabatic change: A change in which the heat of the system remains constant.(∆q = 0) Isobaric change: A change in which the pressure of the system remains constant.(∆P = 0) Isochoric change: A change in which the volume of the system remains constant.(∆V = 0)

10. Law of Conservation of Energy : First Law of Thermodynamics It states that the energy of the universe remains constant during chemical & physical changes. Or, the energy of an isolated system constant. • Mathematical expression for first law of thermodynamics: initial internal energy = U1, heat added = q + w final internal energy (U2)= U1+q+w Now, U2 = U1 + q + w U2 - U1 = q + w

11. Work Irreversible work Reversible work • Change should take place is fast. • In each step the system &surroundings are not always in eqilibrium. • At any stage the system cannot be infinitesimal change. • W irrev = -p∆V • Change should take place in infinitesimal change in small steps. • In each step the system & surroundings are always in near equilibrium with each other. • At any stage the system can be infinitesimal change. • W rev = 2.303nRT log V2/V1

12. Work • Pressure – Volume work If, pex > pin piston moves downwards until pex becomes pin. F =p/A F = pex × A W = (pex × A) × l = pex ×(A ×l) W = Pex × ∆V Also, Vi = initial volume, Vf= final volume ∆V = Vf– Vi w = -pex× ∆V (a) Work done on the system pex pin Length(l) w= -p ∆ V

13. Work • (b) Work done by the system If, pin > pex then, Piston will moves upwards. F = pin × A × l = pin ∆V w = F × l = (pin × A) × l = pin ∆ V = pin(-∆ V) pex pin Length(l)

14. Isothermal & free expansion of an ideal gas ∆U = q +w can be expressed for isothermal irreversible & reversible change as follows; • For isothermal irreversible change q = -w = Pex ( Vf – Vi) • For isothermal reversible change q = -w = nRT ln Vf/Vi = 2.303 nRT log Vf/Vi • For adiabatic change, q = 0 ∆U = wad

15. Enthalpy & Enthalpy Change (1)Enthalpyis sum of internal energy & pressure-volume energy at a particular temperature & pressure. It is also called heat content. H = E + pV H denotes enthalpy. (2) Enthalpy change is the measure of heat change taking during constant temperature and constant pressure . It is denoted by ∆H. ∆U = q + wirrev…(1) =q – p ∆V at constant volume(∆V=0), change in internal energy is equal to change in heat at constant volume. From 1st law of thermodynamics, ∆U = q – p ∆V U2-U1 = qp - p(V2-V1) (U2+pV2) – (U1+pV1) = qp…(2) (final state) (initial state) Let, U + pV = H (H = enthalpy) So, U2 + pV= H2 & U1+ pV = U1 Hence, from (2) H2-H1 = qp So, enthalpy is heat change at pressure

16. Relationship between ∆H & ∆U (1) We know from 1st law of thermodynamics, ∆U =qp– p∆V qp = ∆U + p∆V ∆H = ∆U+ p∆V …(1) (∆H = qp) If the total volume of gaseous reactant is VA and total no. of moles of gaseous reactant is nA. After reaction the total no. of moles and volume of gaseous product is nB and Vbrespectively. aA + bBcC + dD Then , by the ideal gas equation;

17. Relationship between ∆H & ∆U (2) Total vol. of gaseous reactant =VA Total no. of moles of gaseous reactant = nA Total vol. of gaseous product =VB Total no. of moles of gaseous product = nB For reactants (initial state) ; pV = nART …(2) For products (final state) ; pV= nBRT …(3)

18. Relationship between ∆H & ∆U (3) Subtracting (3) from (2) P(VB-VA )= (nB-nA) RT p∆V = ∆ngRT …(4) Substitute (4) in (1) where, ∆H = change in enthalpy ∆U = change in internal energy ∆ng = change in no. of moles of gaseous reactants & products.

19. Macroscopic Properties of the System • The properties of the system which arise from the bulk behavior of matter are called macroscopic properties. • In thermodynamics the macroscopic properties can be divided into two types :

20. Heat capacity: The amount of heat required to raise the temperature of the substance by 1C is known as its heat capacity. q = C∆T (q=heat change, C=heat capacity) • Specific Heat capacity: The amount of heat required to raise the temperature of unit of substance by 1C is known as specific heat capacity. q = mc∆T (mc=specific heat capacity) • Molar Heat capacity: The amount of heat required to raise the temperature of substance by 1C is known as molar heat capacity. cm=(C / n) (cm=molar heat capacity)

21. Relationship between Cp and Cv for an ideal gas (1) Cp= specific heat capacity at constant pressure Cv= specific heat capacity at constant volume R = universal gas constant We know, q = C∆T At constant pressure qp= Cp∆T ∆H = Cp∆T…(1) At constant volume qv= Cv∆T ∆U = Cv∆T…(2)

22. Relationship between Cp and Cv for an ideal gas (2) We know, ∆H = ∆U + p∆V …(3) By substitute (1)&(2) in (3) Cp∆T = Cv∆T + p∆V …(4) From ideal gas equation, pV = RT (for one mole gas) p∆V = R∆T …(5) Now , substitute (5) from (4) Cp∆T = Cv∆T + R∆T

23. Enthalpy of reaction & standard enthalpy of reaction • The enthalpy change taking place during a chemical reaction is known as enthalpy of reaction. rH = enthalpy of reaction. • The enthalpy change taking place during a chemical reaction when all reactants and products are at standard state at that temperature is known as standard enthalpy of reaction. ∆rH° = ∑νP HP - ∑νR HR Sum of enthalpy of products Sum of enthalpy of reactants

24. Standard state • Standard state of any substance at any temperature is its most stable state at that temperature. ∆H = H2-H1 ∆rH = ∑νP HP - ∑νR HR νP = stoichiometric coefficient of products νR = stoichiometric coefficient of reactant s

25. Enthalpy changes during phase transformation • Enthalpy of fusion (∆fusH°): It is enthalpy change taking place during the fusion of 1 mol of solid at its melting point. • E (nthalpy of vaporization ∆vapH°): It is enthalpy change taking place during the vaporization of 1 mol of a liquid at its boiling point.

26. Enthalpy changes during phase transformation • Enthalpy of sublimation (∆subH°): It is enthalpy change when one mole of a solid substance sublimes at a constant temperature and under standard pressure (1bar).

27. Standard enthalpy of formation (∆fH°) • The enthalpy change taking place when one mole of compound is formed from its constituents elements and all are in their standard state. ∆rH° =[sum of standard enthalpy of formation of products]- [ sum of standard enthalpy of formation of reactants]

28. Thermochemical equation • The balanced chemical equation equation which also informs about heat change taking place is known as thermochemicalequation. A thermochemical equation can be written as follows ; (a) by writing the heat evolved or absorbed as a term in the eqation, C(s)+O2(g) CO2(g) +393.5 kJ (b)By using H notation, i.e., writing H = -ve for exothermic and H = +ve for endothermic reactions, as C2H5OH(l) + 3O2 2CO2 + 2H2O : ∆H = -1367 kJ

29. Hess law • The total enthalpy change remains constant whether the process takes place in single step or many steps. C(s) + O2(g) CO2(g) CO2(g) ∆HCO2 = 393.5 kJ/mol +1/2 O2 +1/2 O2 ∆H3 = -283 kJ/mol ∆H2= -110.5 kJ/mol

30. Enthalpy of different types of reactions • Standard enthalpy of combustion(∆cH°): The enthalpy change taking place when one mol of compound is undergoes in complete combution and all reactants and products are in their standard state. • Enthalpy of solution(∆solH°): The enthalpy change taking place when one mol of solute is dissolved in one mol of solvent . • Enthalpy of atomization(∆aH°): The enthalpy change taking place when one mol of solid or molecule or compound is changed into constituents atoms.

31. Born - Haber cycle • Born – Haber cycle is an indirect method to construct an enthalpy digaram. Na(s) + 1/2Cl2(g) NaCl(s) Na(g) Cl(g) Na(g) + Cl(g) ∆fH° = ∆subH + ∆iH + 1/2∆aH + ∆egH + ∆LattH ∆fH° ∆subH 1/2∆aH ∆iH ∆egH ∆Latt H

32. Spontaniety • A process which can take place by itself under the given sets of conditions once it has been initiated if necesarrry, is said to be a spontaneous process. It may be of two types : (a) Spontaneous process where no initiation is needed. e.g. 2NO(g)+O2(g) 2 NO2(g) (b) Spontaneous process where some initiation is required. e.g. CH4(g)+O2(g) CO2(g)+2H2O(l)

33. Entropy • The property of a system which measures the degree of disorder or randomness in the system. it is denoted by S. Entropy is a state function.

34. 2nd law of thermodynamics • The entropy of the universe always increase in the course of every spontaneous change. • In open system the process will be spontaneous if ∆STotal is positive. ∆Stotal = ∆Ssys + ∆Ssurr ∆ST > 0, spontaneous ∆ST = 0, equilibrium ∆ST < 0, non - spontaneous

35. Gibbs energy The maximum amount of energy available to a system during a process that can be converted into useful work is called Gibbs energy. G = Gibbs free energy = H – TS ∆STotal= ∆Ssys+ ∆Ssurr = ∆Ssys + (∆H)surr/T {∆S=qrev/T=∆Hsurr/T } = ∆Ssys + {(-∆H)sys/T} {-(∆H)surr=-(∆H)sys} T∆STotal = T∆Ssys – (∆H)sys (∆H)sys – T∆STotal = - T∆Stotal ∆Gsys = -T∆STotal {∆G=∆H-T∆S}

36. Gibbs energy change & equilibrium • Gibbs energy change of the system may be expressed as ∆G = ∆G° + RT lnK/Qc{ lnK = logeK} At equilibrium, ∆G = 0 0 = ∆G° + RTlnK ∆G° = -RTlogeK {Qc = K}