1.6 Thermodynamics Processes A process means:

change in the condition or state of the system

A path represents a sequence of situations a

system passes through during a change in the state

of the system

Thus the transformation from A →B the system can

go through various parts

1.6.1 Adiabatic Process No heat transfer occurs across the boundary

between the system and its surroundings i.e. the

temperature gradient, ΔT = 0

If ΔT ≠ 0, heat will transfer (which is a rate process)

How adiabatic processes are achieved?

Process is carried out quickly

Well insulated boundary

1.6.2 Isothermal Process Temperature is uniform at every point throughout the

system and remains constant during the entire process

If ΔT = 0, Transfer of heat = 0.

If ΔT ≠ 0, Transfer of heat/work will occur until ΔT = 0.

If the process produces heat

Transfer of heat and/or work across the boundary is

mandatory

How to achieve isothermal process?

Process is carried out very slowly (close to infinity)

Permeable boundary

1.6.3 Isobaric Process

Pressure remains constant throughout the system

during the process

1.6.4 Isochoric Process

Volume remains constant throughout the process.

Achieved by Impermeable and rigid

container/boundary

1.6.5 Cyclic Process The initial and final states of the system are the same

The overall changes in all state variables are = zero.

i.e.

In the process of going through this cycle, the system

may perform work on its surroundings

repeating nature of the process path allows for

continuous operation, making the cycle an important

concept in thermodynamics (heat engines, heat

pumps)

1.6.6 Polytropic process

process that obeys the relation:

where p is the pressure, V is volume, n, the

polytropic index, is any real number, and C is a

constant

1.6.7 Isentropic process

Occurs at constant values of the system’s entropy.

Such processes must be adiabatic, and must also

occur without dissipative effects, or irreversibitities.

Sometimes called the reversible adiabatic process

(2nd Law)

1.6.8 Summary

Process Constraints imposed Quantity exchanged

Isobaric Pressure remains constant

(ΔP=0)

Heat and work may be

exchanged

Isothermal Temperature remains

constant (ΔT=0)

Heat and work may be

exchanged

Isochoric Volume remains constant

(ΔV=0)

no work done. Only

heat is exchanged

Adiabatic System remains insulated

(Q=0)

Only work is

exchanged

Cyclic All variables return to

original value (ΔZ=0)

Heat and work may be

exchanged

1.7 Thermodynamic Equilibrium

The state of a thermodynamic system can be

characterised by its variable only if the system is in

equilibrium with these variable.

Thus a system is in thermodynamic equilibrium only if

it is satisfied all of the conditions;

Mechanical equilibrium: mainly P (in the absence of

electric, magnetic forces).

pressure of the system must be uniform and there must

be no changes in pressure if other variables are not

changed.

Thermal equilibrium: Temperature must be uniform

throughout the system. Thus there will be no tendency

of heat to flow from one part of the system to the other.

For purely physical processes such as

expansion/compression of a substance e.g. H2O

vapour, thermodynamic equilibrium = mech

equilibrium + thermal equilibrium.

However, for physico-chemical processes and

reactive systems, such as those encountered in

extractive metallurgy, there is need for attainment of

chemical equilibrium in addition to the above 2

Chemical equilibrium: Chemical potential of the system

must be uniform i.e. No change in free energy.

Partial/pseudo equilibrium

occurs when a system is not in complete

thermodynamic equilibrium.

There will be very small (undetectable) changes in the

system as it tries to attain equilibrium.

E.g. cementite (Fe3C) in iron-carbon system is

metastable (not completely stable). But it will remain

so for ever for as long as the steel is kept at room

temperature

1.8 The equation of state of an ideal

gas Any equation that relates the pressure (P),

temperature (T), and specific volume (v) of a

substance is called an equation of state.

Property relations that involve other properties of a

substance at equilibrium states are also referred to as

equations of state.

There are several equations of state, some simple

and others very complex

The simplest and best-known equation of state for

substances in the gas phase is the ideal-gas

equation of state.

Predicts the P-v-T behaviour of a gas quite

accurately within some properly selected region

is derived from the following laws;

Boyle’s Law: For a gas at constant temperature

Charles’s Law: For a gas at constant

pressure

These relationships can be plotted on a P-v-T surface

(at constant T we get rectangular hyperbola while at

constant pressure we get straight lines)

Guy Lussac’s Law: the pressure of a fixed amount of gas at fixed volume is directly proportional to its temperature in kelvins

i.e.

Combining the 3 laws gives

That constant can be calculated at STP (1 atm, 273K and 22.4L) to give 8.314 J/mol.K (or kJ/kmol.K), which is the universal gas constant (i.e. it is for all gases) and is denoted by Ru

Thus

… equation of state for 1 mole of ideal gas.

It is called the ideal gas law or the ideal-gas

equation of state and a gas that obeys this

relation is called an ideal gas.

In this equation, P is the absolute pressure, T is

the absolute temperature, and v is the specific

volume.

The gas constant R is different for each gas and

is determined from

The gas constant R is different for each gas and

is determined from

Where M is the molar mass of the gas.

And since mass = molar mass x number of

moles i.e. m = MN

Then the ideal-gas equation of state can be

written in several different forms:

1.9 Zeroth Law

If two systems (say A and B) are in thermal

equilibrium with a third system (say C) separately

(that is A and C are in thermal equilibrium; B and

C are in thermal equilibrium) then they are in

thermal equilibrium themselves (that is A and B

will be in thermal equilibrium

It is the basis of temperature measurement

Thus in order to know if two bodies are at the

same temperature there is no need to bring

them together and observe changes in their

properties

It is necessary only to check if they are

individually in equilibrium with a third body and

this third body is practically a thermometer

In metallurgical thermodynamics the Law may

be applies in studying phases for example

1.10 Work

It is energy transfer across the boundary of a

system that is equivalent to a force acting through

a distance

W>0 : work is done by the system

W<0 : work is done on the system

W=0 : no work done

2

1.dsFW

For a gas, work is the product of the pressure p and

the change in volume V during a process

the pressure will be constant.

2

1

v

vpdVwork

1.11 Energy

it is the capacity to bring about changes in a

system

Microscopic forms of energy are those related to

the energy possessed by the individual

molecules and to the interaction between them

Macroscopic forms of energy on the other hand

are related to the gross characteristics of the

substance on a large scale.

Total energy, Etotal = Emacroscopic + Emicroscopic

Kinetic energy,

It is associated with mass of whole body, thus it

is an extensive property

Potential energy

Dependent on mass of object; thus extensive

Mechanical: Kinetic, potential and

configurational.

Thermal: Heat exchanged.

Electrical: Electrical energy = current x time x

potential difference.

Chemical: Chemical energy = no. of chemical

bonds x bond strength

2

2

1mvEk

mghEp

Internal energy, U : sum of all molecular or

microscopic energies of a substance and is an

extensive property

Internal energy per unit mass, u is an intensive property.

Absolute value of the energy is not known. All we

can determine is change in internal energy.

Internal energy will depend on temperature for a

material of fixed mass, composition and structure.

i.e. U is function of Temperature only.