tp 10 energy of an ideal gas (shared)
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Thermal physics
A-level Physics
Unit G484: The Newtonian World
Mean energy of particles
in an ideal gas
A-level Physics
Unit G484: The Newtonian World
Mean energy of particles
in an ideal gas
Thermal physics
Temperature can be defined as a measure of the ‘hotness’ of a body.
To do
• When we measure the temperature of a gas what is it telling us?
• Recall the assumptions behind an ideal gas: which of them deal
with the energy of its particles?
• Imagine cylinders of hydrogen and oxygen at the same
temperature. What differences – if any – would you notice
between the molecules of gas in each cylinder?
Temperature LOs
Thermal physics
An ideal gas is one that obeys Boyle’s law at all temperatures.
On a microscopic scale, an ideal gas:
• consists of a large number of particles (atoms or molecules) in constant motion at high speed;
• collisions between particles and between particles and the walls of a container are perfectly elastic (kinetic energy is conserved);
• there are no intermolecular forces except during instantaneous collisions;
• the total volume of particles is very small compared with the volume of the container.
A gas fitting this description is called an ‘ideal gas’. Normal gases (especially dilute gases) come close to meeting the description.
Ideal gases: simplifying assumptions LOs
Thermal physics
Learning objectives
At the end of the lesson you will be able to:
• explain that the mean translational kinetic energy of an atom in an ideal gas is directly proportional to the temperature of the gas in kelvin;
• select and apply the equation for the mean translational kinetic energy of atoms.
Lesson focus• Mean energy of particles in an ideal gas
Thermal physics
Learning outcomes
All of you should be able to
• describe the energy of an ideal gas;
• explain what temperature tells us about a gas;
• recall the link between the kinetic energy of an ideal gas and its temperature;
• solve simple problems concerning the energy of an ideal gas.
Most of you should be able to• solve more complex problems concerning the energy of an ideal gas.
Thermal physics
The pressure of an ideal gas is given by the following equation:
p = ⅓ ρ‹c2› where, ρ - density ‹c2› - ‘mean squared speed’
of gas particles
To do• Using this equation, derive an expression starting ‘ pV = … ’
[hints: ρ = ? total mass of gas, M = ? ]
• Now equate your expression with one form of the ideal gas equation.
The meaning of temperature LOs
LO 1: explain that the mean translational kinetic energy of an atom in an ideal gas is directly proportional to the temperature of the gas in kelvin
Thermal physics
The mean translational kinetic energy of a particle in an ideal gas is related to absolute temperature in the following way:
p = ⅓ ρ‹c2›
= ⅓ ‹c2› M - total mass of gas
= ⅓ ‹c2› N - number of particles
m - mass of each particle
i.e. pV = ⅓ Nm ‹c2›
= NkT
kT = ⅓ m ‹c2›
kT = ⅓ m ‹c2› = ½ m ‹c2›
LO 1: explain that the mean translational kinetic energy of an atom in an ideal gas is directly proportional to the temperature of the gas in kelvin
The meaning of temperature LOs
Thermal physics
Key result
The mean kinetic energy of a gas particle is directly proportional to the
absolute (kelvin) temperature of the gas.
i.e. Ek T
Note
This equation describes the translational kinetic energy of particles in a monatomic gas. Diatomic (or other non-monatomic) gases also possess rotational and vibrational k.e..
The meaning of temperature LOs
LO 1: explain that the mean translational kinetic energy of an atom in an ideal gas is directly proportional to the temperature of the gas in kelvin
½ m‹c2› = kT