Page 1 of 6 SPH 2202 – Thermal Physics I Lecture notes

Introduction
Unit code and name: SPH 2202 – Thermal Physics I
 Thermal Physics – the study of thermal energy (heat energy).
Thermal energy – energy possessed by an object due to movement of particles within it.
Heat results from the motion of particles within matter.

 Thermal Physics may be viewed from two dimensions:

o Macroscopic approach
→ No reference is made to the internal state of matter.
→ Only the effects of the action of atoms or molecules are considered, as
perceived by human senses. For instance, volume may be approximated by
sight or measurement, temperature may be deduced by touch or measurement,
etc.
o Microscopic approach
→ Gives reference to the internal state of matter.
→ Knowledge of the behavior of the atoms or molecules is required.

o Statistical Mechanics - the study of thermal physics by use of a microscopic

approach.
o Thermodynamics – the study of thermal physics from a macroscopic approach.

This course shall only dwell on Thermodynamics.

 Thermodynamics – aim: To establish a relationship between macroscopic quantities and

the processes resulting from changes in them.
 Principles of thermodynamics - widely applied in:
o Boilers - heated or vaporized fluid is used in various processes including cooking,
central heating, boiler-based power generation (thermal power plants), etc.
o Nuclear power plants, hydroelectric power plants, etc.
o Refrigerators and deep freezers, air-conditioning systems, etc.
o Gas compressors, blowers, fans, etc.
o Radiators, coolers, heaters – heat transfer methods.
o Rocket propulsion.
o Steam in industry - evaporating water to concentrate solids in a solution, drying out a
solid product, cracking - producing lighter fuels, distillation.

NB: Supplement your learning from the lecture and lecture notes by independent study and discussions.
Page 2 of 6 SPH 2202 – Thermal Physics I Lecture notes
Course outline

 Important terms: thermodynamic system, thermal interaction, surrounding, universe,

open/closed thermodynamic systems, diathermic/adiabatic wall, permeable/impermeable
wall, isolating/non-isolating wall, thermodynamic variables, states and process,
thermodynamic equilibrium, equation of state, important mathematical theorems.
 Simple thermodynamic systems: hydrostatic system - volume expansivity, isothermal
compressibility/incompressibility. Stretched wire - linear expansivity, isothermal Young’s
modulus. Surfaces. Electrochemical cell. Extensive and intensive variables.
 The zeroth (0th) law of thermodynamics: the concept of temperature, temperature scales and
thermometers, the equation of state.
 Thermodynamic work: reversible and irreversible transformations, adiabatic and isothermal
processes, work done in a simple thermodynamic system.
 The first (1st) law of thermodynamics: the concept of heat, heat capacity, specific heat
capacity, heat transfer methods; conduction – thermal conductivity; convection; radiation –
blackbody radiation, Prevost’s theory of exchanges, Stefan-Boltzmann law, applications of
the first law of thermodynamics.

Reference books

1. Halliday D. and Resnick R., 1995. Physics II, John Willey and sons Inc, New York.
2. Seers and Zemansky, University Physics.
3. Griffiths D.J., 1991. Introduction to Electrodynamics, Prentice Hall International Inc,.
Toronto.

Course assessment

1. Continuous assessment 30%:

i. Tests (CATs) 15%
ii. Practicals 10%
iii. Assignments 5%
2. Final ordinary university examination 70%.

NB: Supplement your learning from the lecture and lecture notes by independent study and discussions.
Page 3 of 6 SPH 2202 – Thermal Physics I Lecture notes
Definition of important terms and theorems

 Thermodynamic system - a quantity of fixed mass under investigation e.g. a potato.

 Surrounding – everything external to the thermodynamic system.
 System boundary – interface separating the thermodynamic system and its surrounding.

 Universe – combination of thermodynamic system and its surroundings.

 An open thermodynamic system – it allows the exchange of matter and energy (heat) between
it and its surrounding.
 A closed thermodynamic system – it does not allow the exchange of matter between it and the
surrounding but allows exchange of energy.

 An isolated thermodynamic system – it’s not influenced by its surrounding.

 Wall - the boundary that separates a thermodynamic system from its surrounding. It can be:
o Diathermic or adiabatic (figure below) – a diathermic wall permits flow of heat (while
preventing the flow of matter) and an adiabatic wall does not permit flow of heat and also
prevents the flow of matter.

A system enclosed within an adiabatic wall, therefore, is isolated.

NB: Supplement your learning from the lecture and lecture notes by independent study and discussions.
Page 4 of 6 SPH 2202 – Thermal Physics I Lecture notes
o Permeable or impermeable – a permeable wall permits the transfer of matter while an
impermeable wall does not.

 Thermodynamic variables - measurable properties of a thermodynamic system that describe

its momentary condition.
Also called thermodynamic coordinates or parameters.
Examples include pressure, temperature, volume, mass, density, etc.
They differ from one system to another. For instance,
o The state of a gas enclosed in a vessel is described by its pressure, volume, temperature
and mass.
o The state of a metal bar is described by its length, cross-section, tension, temperature.
o The state of a liquid film is described by its area, surface tension, etc.
 Thermodynamic state - a set of thermodynamic variables that can be used to fully define the
status of a thermodynamic system.
The state of a thermodynamic system depends on whether or not there is an interaction (via
matter and energy exchange) between it and its surrounding. Its state remains unchanged when
there is no interaction between it and its surrounding. Otherwise, its state undergoes a change
whenever there is an interaction between it and its surrounding.
 Thermal interaction – energy exchange between two thermodynamic systems that are in
physical contact. Such systems are therefore said to be in thermal contact.
 Thermodynamic process – when a thermodynamic system changes from one state to another
as a result of the exchange of energy with the surrounding (or other systems).
 Initial state - the state of a thermodynamic system at the beginning of a thermodynamic process
 Final state – the state of a thermodynamic system and at the end of a thermodynamic process.
 End states – collective term for the initial and final states of a thermodynamic process.
 Thermodynamic equilibrium – determined by the interaction by a thermodynamic system and
its surrounding.
A thermodynamic system is said to be in a state of:

i. Mechanical equilibrium when all the forces either in its interior or between it and its
surrounding are balanced.
ii. Chemical equilibrium when, in addition to being in a state of mechanical equilibrium, it
does not undergo any chemical reaction or transfer of matter through, say, diffusion.
iii. Thermal equilibrium when, in addition to being in a state of mechanical and chemical
equilibrium, it does not undergo any changes in its state variables.
iv. Thermodynamic equilibrium after it attains mechanical, chemical and thermal
equilibrium.

NB: Supplement your learning from the lecture and lecture notes by independent study and discussions.
Page 5 of 6 SPH 2202 – Thermal Physics I Lecture notes
o If the conditions given for each equilibrium type are not satisfied, a change of state must
take place until equilibrium is reached.
o When a system is in thermodynamic equilibrium its parameters are such that if one of them
is changed the system accommodates the new value (of the parameter that changed) by
changing some other of its parameters. For instance, if it’s the pressure that changes, the
system may change, say the volume, to accommodate the new value of the pressure.

 Important mathematical formulations used in thermodynamics

o Let x, y, z be the thermodynamic variables of a simple thermodynamic system and each
one be expressible in terms of the remaining two i.e. x = x(y, z), y = y(x, z), z = z(x, y).
o From the functions of x and y we get,

𝜕𝑥 𝜕𝑥
𝑑𝑥 = ( ) ∙ 𝑑𝑦 + ( ) ∙ 𝑑𝑧 ---------------------------------------------------------------------- 1
𝜕𝑦 𝜕𝑧
𝑧 𝑦

𝜕𝑦 𝜕𝑦
𝑑𝑦 = ( ) ∙ 𝑑𝑥 + ( ) ∙ 𝑑𝑧 ---------------------------------------------------------------------- 2
𝜕𝑥 𝜕𝑧
𝑧 𝑥

 Substitute eq. 2 into eq. 1 and re-arrange,

𝜕𝑥 𝜕𝑦 𝜕𝑥 𝜕𝑦 𝜕𝑥
[1 − (𝜕𝑦) ∙ (𝜕𝑥 ) ] ∙ 𝑑𝑥 = [(𝜕𝑦) ∙ ( 𝜕𝑧 ) + (𝜕𝑧 ) ] ∙ 𝑑𝑧 --------------------------------- 3
𝑧 𝑧 𝑧 𝑥 𝑦

 Suppose that two neighboring equilibrium states have the same value of z, i.e. dz = 0, then, eq.
3 becomes,
𝜕𝑥 𝜕𝑦
[1 − ( ) ∙ ( ) ] ∙ 𝑑𝑥 = 0
𝜕𝑦 𝑧 𝜕𝑥 𝑧
or

𝜕𝑥 1
(𝜕𝑦) = 𝜕𝑦 --------------------------------------------------------------4
𝑧 ( )
𝜕𝑥 𝑧

Similarly, it can be shown that,

o From the functions of 𝑦 and 𝑧 we get,
𝜕𝑦 1
( 𝜕𝑧 ) = 𝜕𝑧 -----------------------------------------------------------------5
𝑥 ( )
𝜕𝑦 𝑥

NB: Supplement your learning from the lecture and lecture notes by independent study and discussions.
Page 6 of 6 SPH 2202 – Thermal Physics I Lecture notes
o From the functions of 𝑥 and 𝑧 we get,
𝜕𝑧 1
(𝜕𝑥) = 𝜕𝑥 -----------------------------------------------------------------6
𝑦 ( )
𝜕𝑧 𝑦

Eq. 4 – 6 ≡ reciprocal rule.

 Suppose that two neighboring equilibrium states have the same value of x, i.e. dx = 0, then,
eq. 3 becomes,
𝜕𝑥 𝜕𝑦 𝜕𝑥
(𝜕𝑦 ) ∙ ( 𝜕𝑧 ) = − (𝜕𝑧 )
𝑧 𝑥 𝑦

or
𝜕𝑥 𝜕𝑦 1
(𝜕𝑦 ) ∙ ( 𝜕𝑧 ) ∙ 𝜕𝑥 = −1
𝑧 𝑥 ( )
𝜕𝑧 𝑦

1 𝜕𝑧
Substitute 𝜕𝑥 with ( ) (from eq. 6),
( ) 𝜕𝑥 𝑦
𝜕𝑧 𝑦

𝜕𝑥 𝜕𝑦 𝜕𝑧
(𝜕𝑦) ∙ ( 𝜕𝑧 ) ∙ (𝜕𝑥) = −1 --------------------------------------------7
𝑧 𝑥 𝑦

Eq. 7 → cyclic permutation rule

 If the variables x, y, z denote pressure P, volume V, and temperature T, respectively then eq. 7
takes the form,
𝜕𝑃 𝜕𝑉 𝜕𝑇
( ) ∙ ( ) ∙ ( ) = −1
𝜕𝑉 𝑇 𝜕𝑇 𝑃 𝜕𝑃 𝑉

NB: Supplement your learning from the lecture and lecture notes by independent study and discussions.