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

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.

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 Matter

Matter

Energy

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 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

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

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 × ∆VAlso, Vi = initial volume, Vf = final volume ∆V = Vf – Vi

w = -pex × ∆V

(a) Work done on the system

pin

Length(l)

w= -p ∆ V

pex

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)

pin

pex

Length(l)

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

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 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

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 Vb

respectively. aA + bB cC + dD

Then , by the ideal gas equation;

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)

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.

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 :

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)

Relationship between Cp and Cv for an ideal gas (1) Cp = specific heat capacity at constant pressureCv = specific heat capacity at constant volumeR = universal gas constant

We know, q = C∆TAt constant pressure qp = Cp∆T ∆H = Cp∆T …(1) At constant volume qv = Cv∆T ∆U = Cv∆T …(2)

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

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

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

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.

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).

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]

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) +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

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

∆H2= -110.5 kJ/mol

∆H3 = -283 kJ/mol+1/2 O2 +1/2 O2

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.

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

∆Latt H

∆iH ∆egH

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)

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.

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

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}

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}