Thermodynamics

Thermodynamic Terms

1 System If refers to the part of universe in which observations are carried out.

2 Surroundings The part of universe other than the system is known as surroundings.

3 Boundary The wall that separates the system from the surroundings is called boundary.

4 Thermodynamic equilibrium A system in which the macroscopic properties do not undergo any change with time is called thermodynamic equilibrium.

5 Thermal equilibrium If there is no flow of heat from one portion of the system to another, the system is said to be in thermal equilibrium.

6 Mechanical equilibrium If no mechanical work is done by one part of the system on another part of the system, it is said to be in mechanical equilibrium. Such a condition exists when pressure remains constant.

Types of Systems

1 Open system The system in which energy and matter both can be exchanged with the surroundings.

2 Closed system The system in which only energy can be exchanged with the surroundings.

3 Isolated system The system in which neither energy nor matter can be exchanged with the surroundings.

State of System

When microscopic properties have definite value, the conditions of existence of the system is known as state of system.

State functions (State variables) When values of a system is independent of path followed and depend only on initial and final state, it is know as state function, e.g. ∆U, ∆H, ∆G etc.

Path functions These depend upon the path followed, e.g. work, heat, etc.

Thermodynamic Properties

1. Intensive Properties

Properties of the system which depend only on the nature of matter but not on the quantity of matter are called intensive properties, e.g. pressure, temperature, specific heat, etc.

2. Extensive Properties

Properties of the system which are dependent on the quantity of matter are called extensive properties, e.g. internal energy, volume, enthalpy, etc.

Internal Energy (E or U)

It is the total energy within the substance. It is the sum of many types of energies like vibrational energy, translational energy, etc. It is a extensive property and state function.

Its absolute value cannot be determined but experimentally change in internal energy (∆U) can be determined by

∆U = U2 – U1 or ∑UP - ∑UP

For exothermic process, ∆U = -ve, whereas for endothermic process ∆U = +ve.

U depends on temperature, pressure, volume and quantity of matter and is independent of the method by which state has been attained.

Zeroth Law of Thermodynamics or Law of Thermal Equilibrium

The law states that if the two systems are in thermal equilibrium with a third system then they are also in thermal equilibrium with each other. Temperature is used here to know, the system is in thermal equilibrium or not.

First Law of Thermodynamics

Energy can neither be created nor destroyed although it can be converted from one form to the other.

Mathematically, ∆U = q + W

where, ∆U = internal energy change

q = heat added to system

W = work added to system

Sign convention

1 q is +ve = heat is supplied to the system

2 q is –ve = heat is lost by system

3 W is +ve = work done on the system

4 W is –ve = work done by he system.

Modes of Transference of Energy

Heat (q)

It occurs when there is a difference of temperature between system and surroundings. It is a random form of energy and path dependent.

Its units are joule or calorie.

It is given as, q = mc∆t

where, m = mass of substance,

c = specific heat

∆t = temperature difference

Work (W)

If the system involves gaseous substance and there is a difference of pressure between system and surroundings, work is referred as pressure-volume work (WpV).

Expression for Pressure volume work

Work of irreversible expansion against constant pressure p under isothermal conditions

q = -WpV = pext∆V

Work of reversible expansion under isothermal conditions

q = -Wrev = 2.303 nRT log (V2/V1)

or q = -Wrev = 2.303 nRT log p1/p2

Work of reversible expansion under adiabatic condition

$W_{rev}=\frac{nR}{\gamma -1}\left(T_2-T_1\right)$

where, $\gamma$ = Poisson's ratio

(Under adiabatic conditions $T{V}^{\gamma -1}$ = constant)

Work of irreversible expansion under adiabatic conditions

$W_{irrev}=-P_{ext}\times R\left[\frac{p_1{T}_2-p_2{T}_1}{p_1{p}_2}\right]$

When an ideal gas expands in vacuum then

pext = 0

Work done is maximum in reversible conditions.

Units: CGS system – erg

SI system – joule

[work and heat both appear only at the boundary of the system during a change in state.]

Thermodynamic Process

It is the operation which brings change in the state of the system. Thermodynamic processes are

1 Isothermal process In which temperature remains constant, i.e. (dT = 0, ∆U = 0).

2 Isochoric process In which volume remains constant, i.e. (∆V = 0).

3 Isobaric process In which pressure remains constant, i.e. (∆p = 0)

4 Adiabatic process In which heat is not exchanged by system with the surroundings, i.e. (∆q = 0).

5 Cyclic process It is a process in which system returns to its original state after undergoing a series of change, i.e. ∆Ucyclic = 0; ∆Hcyclic = 0.

6 Reversible process A process that follows the reversible path, i.e. the process which occurs in infinite number of steps in this way that the equilibrium conditions are maintained at each step, and the process can be reversed by infinitesimal change in the state of functions.

7 Irreversible process The process which cannot be reversed and amount of energy increases. All natural processes are irreversible.

Heat Capacity of a System

Heat capacity (c) of system is defined as the amount of heat required to raise the temperature of a system by 1ºC.

1 Molar Heat Capacity

It is the heat capacity of 1 mole of substance of the system.

1 Specific Heat Capacity

It is the heat capacity of 1 g of substance of the system.

Q = mc∆T,

where, m = mass of substance, c = specific heat or heat capacity

Molar heat capacity, at constant pressure,

Cp = cp × M

Molar heat capacity, at constant volume,

Cv = cv × M

(cp and cv are specific heats at constant pressure and constant volume respectively and M is molecular weight of gas)

cp – cv = R (R = Molar gas constant)

Cp – Cv = R/M

The molar heat capacity at constant volume,

CV = (3/2) R

The molar heat capacity at constant pressure,

$C_p=\left(\frac{3}{2}\right)R+R=\left(\frac{5}{2}\right)R$

Poisson's ratio, $\gamma =\frac{C_p}{C_V}=\left(\frac{5}{3}\right)=1.66$

$\gamma$ = 1.66 for monoatomic gas

$\gamma$ = 1.40 for diatomic gas

$\gamma$ = 1.33 for triatomic gas

Enthalpy (H)

It is the sum of internal energy and pV-energy of the system. It is a state function and extensive property. Mathematically,

H = U + pV

Like U, absolute value of H also cannot be know, ∆H is determined experimentally.

∆H = H2 – H1

or $\Sigma H_P=\Sigma H_R$

For exothermic reaction (the reaction in which heat is evolved), ∆H = -ve whereas for endothermic reaction (the reaction in which heat is absorbed), ∆H = +ve.

Relationship between ∆H and ∆U

∆H = ∆U + ∆p∆V

or ∆H = ∆U + ∆n(g)Rt

Here, ∆ng = change in the number of gas moles.

Enthalpy change or Reaction Enthalpy (∆fH)

It is the change in enthalpy that accompanies a chemical reaction represented by a balance chemical equation.

${\Delta }_{r}H=\Sigma H_{\left(P\right)}-\Sigma H_{\left(R\right)}$

Enthalpy of reaction expressed at the standard state conditions is called standard enthalpy of reaction $\left(\Delta H^{\ominus }\right)$.

Factors affecting enthalpy of reaction

1 Physical state of reactants and products.

2 Allotropic forms of elements involved.

3 Chemical composition of reactants and products.

4 Amount of reactants.

5 Temperature.

Various Forms of Enthalpy of Reaction

Enthalpy of Formation ($\Delta H_f^{\ominus }$)

It is the heat change when one mole of compound is obtained from its constituent elements. Enthalpy of formation at standard state is known as standard enthalpy of formation ${\Delta }_{f}H$ and is taken as zero by convention.

Enthalpy of Combustion (${\Delta }_c{H}_{}^{\ominus }$)

It is the enthalpy change taking place when one mole of a compound undergoes complete combustion in the presence of oxygen ($\Delta H_C$).

$\Delta H_C$ is always negative, because process of combustion is exothermic.

Enthalpy of Solution $\left({\Delta }_{sol}{H}^{\ominus }\right)$

${\Delta }_{sol}{H}^{\ominus }={\Delta }_{lattice}{H}^{\ominus }+{\Delta }_{hyd}{H}^{\ominus }$