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

System & Surroundings SystemSurroundings  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

Types of System:

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. System MatterEnergy Matter Energy Surroundings Matter

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.

Internal energy and internal energy change Internal energy (U) The energy associated with the system at a particular conditions of temperature and pressure. Internal energy change (∆U) It is measure of heat change occurring during the process at constant temperature & volume. q v = ∆U

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

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.

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

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 qw∆U Change in internal energy Heat added to the system Work done on the system

Work Irreversible workReversible 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

Work  Pressure – Volume work If, p ex > p in piston moves downwards until p ex becomes pin. F =p/A F = p ex × A W = (p ex × A) × l = p ex ×(A ×l) W = P ex × ∆V Also, V i = initial volume, V f = final volume ∆V = V f – V i w = -p ex × ∆V (a) Work done on the system p in Length(l) w= -p ∆ V p ex

Work  (b) Work done by the system If, p in > p ex then, Piston will moves upwards. F = p in × A × l = p in ∆V w = F × l = (p in × A) × l = p in ∆ V = p in (-∆ V) p in p ex Length(l) w = -p in ∆ V

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 = nRT log Vf/Vi  For adiabatic change, q = 0 ∆U = w ad

Enthalpy & Enthalpy Change (1) Enthalpy is 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 + w irrev …(1) =q – p ∆V at constant volume(∆V=0), change in internal energy is equal to change in heat at constant volume. From 1 st law of thermodynamics, ∆U = q – p ∆V U2-U1 = q p - p(V2-V1) (U2+pV2) – (U1+pV1) = q p …(2) (final state) (initial state) Let, U + pV = H (H = enthalpy) So, U2 + pV= H2 & U1+ pV = U1 Hence, from (2) H2-H1 = q p So, enthalpy is heat change at pressure ∆H =q p

Relationship between ∆H & ∆U (1) We know from 1 st law of thermodynamics, ∆U = q p – p∆V q p = ∆U + p∆V ∆H = ∆U+ p∆V …(1) (∆H = qp) If the total volume of gaseous reactant is V A and total no. of moles of gaseous reactant is n A. After reaction the total no. of moles and volume of gaseous product is n B and V b respectively. aA + bB cC + dD Then, by the ideal gas equation;

Relationship between ∆H & ∆U (2) Total vol. of gaseous reactant =V A Total no. of moles of gaseous reactant = n A Total vol. of gaseous product =V B Total no. of moles of gaseous product = n B For reactants (initial state) ; pV = n A RT …(2) For products (final state) ; pV= n B RT …(3)

Relationship between ∆H & ∆U (3) Subtracting (3) from (2) P(V B -V A )= (n B -n A ) RT p∆V = ∆n g RT …(4) Substitute (4) in (1) where, ∆H = change in enthalpy ∆U = change in internal energy ∆n g = change in no. of moles of gaseous reactants & products. ∆H=∆U+∆n g RT

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 : The properties which depends upon quantity of matter present in system. e.g. mass, volume etc. Extensive properties The properties which does not depend upon the quantity of matter present in the system. e.g. temperature, viscosity etc. Intensive properties

 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 = m c ∆ T (m c =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. c m =(C / n) (c m =molar heat capacity)

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

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

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° = ∑ν P H P - ∑ν R H R Sum of enthalpy of products Sum of enthalpy of reactants

Standard state  Standard state of any substance at any temperature is its most stable state at that temperature. ∆H = H2-H1 ∆ r H = ∑ν P H P - ∑ν R H R ν P = stoichiometric coefficient of products ν R = stoichiometric coefficient of reactant s

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

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

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

Thermochemical equation  The balanced chemical equation equation which also informs about heat change taking place is known as thermochemical equation. 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) 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 = kJ

Hess law  The total enthalpy change remains constant whether the process takes place in single step or many steps. C(s) + O 2 (g) CO 2 (g) CO 2 (g) ∆ H CO 2 = kJ/mol ∆ H2= kJ/mol ∆ H3 = -283 kJ/mol +1/2 O 2

Enthalpy of different types of reactions  Standard enthalpy of combustion( ∆ c H° ): 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( ∆ sol H° ): The enthalpy change taking place when one mol of solute is dissolved in one mol of solvent.  Enthalpy of atomization( ∆ a H° ): The enthalpy change taking place when one mol of solid or molecule or compound is changed into constituents atoms.

Born - Haber cycle  Born – Haber cycle is an indirect method to construct an enthalpy digaram. Na(s) + 1/2Cl 2 (g) NaCl(s) Na(g) Cl(g) Na(g) + Cl(g) ∆ f H ° = ∆ sub H + ∆ i H + 1/2 ∆ a H + ∆ eg H + ∆ Latt H ∆fH°∆fH° ∆ sub H1/2 ∆ a H ∆ Latt H ∆iH∆iH ∆ eg H

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 NO 2 (g) (b) Spontaneous process where some initiation is required. e.g. CH4(g)+O2(g) CO2(g)+2H2O(l)

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.

2 nd 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 ∆ S Total is positive. ∆S total = ∆S sys + ∆S surr ∆S T > 0, spontaneous ∆S T = 0, equilibrium ∆S T < 0, non - spontaneous

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 ∆ S Total = ∆ S sys + ∆ S surr = ∆ S sys + ( ∆ H) surr /T { ∆ S=q rev /T= ∆ H surr /T } = ∆ S sys + {(- ∆ H) sys /T} {-( ∆ H) surr =-( ∆ H) sys } T ∆ S Total = T ∆ S sys – ( ∆ H) sys ( ∆ H) sys – T ∆ S Total = - T ∆ S total ∆ G sys = -T ∆ S Total { ∆ G= ∆ H-T ∆ S}

Gibbs energy change & equilibrium  Gibbs energy change of the system may be expressed as ∆ G = ∆ G ° + RT lnK/Q c { lnK = log e K} At equilibrium, ∆ G = 0 0 = ∆G° + RTlnK ∆ G ° = -RTlog e K {Q c = K} ∆ G ° = RT log 10 K