UNIVERSITY OF SOUTH AFRICA
College of Science, Engineering and Technology
PHY3703
Statistical and Thermal Physics
Formative Assessment 1
Prescribed Textbook: Harvey Gould and Jan Tobochnik,
Statistical and Thermal Physics with Computer Applications,
Princeton University Press, 2010
Problems Covered: 1.5, 1.10, 2.4, 2.30
Submission Date: As per myUnisa
Submitted in partial fulfilment of the requirements for PHY3703
, Statistical and Thermal Physics PHY3703 – Assessment 1
Problem 1.5 Nature of Temperature
(a) What is temperature? What reasons do you have for thinking it has
something to do with energy?
Temperature is a macroscopic quantity that describes the thermal state of a system. It
tells us, in a very practical sense, which direction heat will flow when two objects are
brought into contact. The object that loses energy is the hotter one; the object that gains
it is the cooler one. That alone hints at the connection to energy.
At the microscopic level, the link becomes clearer. For an ideal gas, the average transla-
tional kinetic energy of a single molecule is directly proportional to the absolute temper-
ature:
3
⟨Ek ⟩ = kB T
2
where kB is Boltzmann’s constant and T is the temperature in kelvin. So raising the
temperature of a gas literally means speeding up its molecules. The energy is right there
in the motion.
Thermodynamics makes this precise through the definition:
1 ∂S
=
T ∂U V,N
This says temperature is the rate at which entropy changes with internal energy. In other
words, T and U are not just loosely related – they are formally connected through this
partial derivative. When you add energy to a system and its entropy rises, the temperature
is what characterises how quickly that happens.
A few concrete reasons to believe temperature and energy are linked:
Adding heat (a form of energy) to most substances raises their temperature.
Higher temperature gases exert more pressure – their molecules carry more kinetic
energy and hit container walls harder.
Heat flows spontaneously from hot to cold, which is a flow of energy from a region of
higher average molecular motion to one of lower average molecular motion.
At absolute zero (T = 0 K), classical theory predicts no thermal motion at all – the
system is in its lowest possible energy state.
(b) If you add energy to a pot of boiling water, does the temperature of the
water change?
No, the temperature does not change while the water is actively boiling.
At the boiling point (100◦ C at standard pressure), water undergoes a first-order phase
transition from liquid to vapour. Any energy added during this process goes entirely into
breaking the intermolecular bonds that hold water molecules together in the liquid phase.
This energy is called the latent heat of vaporisation, Lv ≈ 2260 J/g for water.
1
College of Science, Engineering and Technology
PHY3703
Statistical and Thermal Physics
Formative Assessment 1
Prescribed Textbook: Harvey Gould and Jan Tobochnik,
Statistical and Thermal Physics with Computer Applications,
Princeton University Press, 2010
Problems Covered: 1.5, 1.10, 2.4, 2.30
Submission Date: As per myUnisa
Submitted in partial fulfilment of the requirements for PHY3703
, Statistical and Thermal Physics PHY3703 – Assessment 1
Problem 1.5 Nature of Temperature
(a) What is temperature? What reasons do you have for thinking it has
something to do with energy?
Temperature is a macroscopic quantity that describes the thermal state of a system. It
tells us, in a very practical sense, which direction heat will flow when two objects are
brought into contact. The object that loses energy is the hotter one; the object that gains
it is the cooler one. That alone hints at the connection to energy.
At the microscopic level, the link becomes clearer. For an ideal gas, the average transla-
tional kinetic energy of a single molecule is directly proportional to the absolute temper-
ature:
3
⟨Ek ⟩ = kB T
2
where kB is Boltzmann’s constant and T is the temperature in kelvin. So raising the
temperature of a gas literally means speeding up its molecules. The energy is right there
in the motion.
Thermodynamics makes this precise through the definition:
1 ∂S
=
T ∂U V,N
This says temperature is the rate at which entropy changes with internal energy. In other
words, T and U are not just loosely related – they are formally connected through this
partial derivative. When you add energy to a system and its entropy rises, the temperature
is what characterises how quickly that happens.
A few concrete reasons to believe temperature and energy are linked:
Adding heat (a form of energy) to most substances raises their temperature.
Higher temperature gases exert more pressure – their molecules carry more kinetic
energy and hit container walls harder.
Heat flows spontaneously from hot to cold, which is a flow of energy from a region of
higher average molecular motion to one of lower average molecular motion.
At absolute zero (T = 0 K), classical theory predicts no thermal motion at all – the
system is in its lowest possible energy state.
(b) If you add energy to a pot of boiling water, does the temperature of the
water change?
No, the temperature does not change while the water is actively boiling.
At the boiling point (100◦ C at standard pressure), water undergoes a first-order phase
transition from liquid to vapour. Any energy added during this process goes entirely into
breaking the intermolecular bonds that hold water molecules together in the liquid phase.
This energy is called the latent heat of vaporisation, Lv ≈ 2260 J/g for water.
1
