UNIVERSITY OF SOUTH AFRICA (UNISA)
College of Science, Engineering and Technology
⋄
FORMATIVE ASSESSMENT 1
Semester 1 — 2026
⋄
Module Code: PHY3703
Module Name: Statistical and Thermal Physics
Assignment No.: 01
Due Date: 2026
Semester: Semester 1, 2026
Submitted in partial fulfilment of the requirements for PHY3703:
Statistical and Thermal Physics at the University of South Africa.
, UNISA | PHY3703 Assessment 1 — 2026
Problem 1.5: Nature of Temperature
Temperature is one of the most fundamental concepts in thermodynamics. Understanding
what it represents physically, and why it is connected to energy, is the starting point for all
further study in thermal physics (Gould and Tobochnik, 2010:3).
(a) What Temperature Is and Why It Is Related to Energy
Temperature is a macroscopic quantity that characterises the thermal state of a system. At
the microscopic level, it measures the average kinetic energy of the constituent particles. For
a monatomic ideal gas, this relationship takes the explicit form:
3
⟨Ekin ⟩ = kB T (1)
2
where kB = 1.381 × 10−23 J/K is Boltzmann’s constant and T is the absolute temperature in
kelvin. Equation 1 is a direct consequence of the equipartition theorem, which assigns 12 kB T
of average energy to each quadratic degree of freedom (Gould and Tobochnik, 2010:14).
In the thermodynamic framework, temperature is defined rigorously through the relationship
between entropy S and internal energy U :
1 ∂S
= (2)
T ∂U V,N
This definition captures why temperature governs the direction of spontaneous energy trans-
fer. A system that gains many accessible microstates per joule added is at a low temper-
ature, while one that gains few is at a high temperature. Energy therefore flows from high-
temperature to low-temperature systems because doing so increases the total number of
microstates available to the combined system, which is the condition for increasing total
entropy (Gould and Tobochnik, 2010:97).
The reasons for associating temperature with energy are as follows. First, supplying heat to
most systems raises their temperature, which corresponds directly to faster average particle
motion. Second, absolute zero (T = 0 K) represents the lowest possible energy state, where
classical motion ceases entirely. Third, when two bodies at different temperatures are placed
in thermal contact, energy flows until they reach the same temperature, a process driven
Page 1 of 13
College of Science, Engineering and Technology
⋄
FORMATIVE ASSESSMENT 1
Semester 1 — 2026
⋄
Module Code: PHY3703
Module Name: Statistical and Thermal Physics
Assignment No.: 01
Due Date: 2026
Semester: Semester 1, 2026
Submitted in partial fulfilment of the requirements for PHY3703:
Statistical and Thermal Physics at the University of South Africa.
, UNISA | PHY3703 Assessment 1 — 2026
Problem 1.5: Nature of Temperature
Temperature is one of the most fundamental concepts in thermodynamics. Understanding
what it represents physically, and why it is connected to energy, is the starting point for all
further study in thermal physics (Gould and Tobochnik, 2010:3).
(a) What Temperature Is and Why It Is Related to Energy
Temperature is a macroscopic quantity that characterises the thermal state of a system. At
the microscopic level, it measures the average kinetic energy of the constituent particles. For
a monatomic ideal gas, this relationship takes the explicit form:
3
⟨Ekin ⟩ = kB T (1)
2
where kB = 1.381 × 10−23 J/K is Boltzmann’s constant and T is the absolute temperature in
kelvin. Equation 1 is a direct consequence of the equipartition theorem, which assigns 12 kB T
of average energy to each quadratic degree of freedom (Gould and Tobochnik, 2010:14).
In the thermodynamic framework, temperature is defined rigorously through the relationship
between entropy S and internal energy U :
1 ∂S
= (2)
T ∂U V,N
This definition captures why temperature governs the direction of spontaneous energy trans-
fer. A system that gains many accessible microstates per joule added is at a low temper-
ature, while one that gains few is at a high temperature. Energy therefore flows from high-
temperature to low-temperature systems because doing so increases the total number of
microstates available to the combined system, which is the condition for increasing total
entropy (Gould and Tobochnik, 2010:97).
The reasons for associating temperature with energy are as follows. First, supplying heat to
most systems raises their temperature, which corresponds directly to faster average particle
motion. Second, absolute zero (T = 0 K) represents the lowest possible energy state, where
classical motion ceases entirely. Third, when two bodies at different temperatures are placed
in thermal contact, energy flows until they reach the same temperature, a process driven
Page 1 of 13
