(ADVANCED PHYSICS TOPIC)
Kinetic Theory
Kinetic theory of gases assumes that:
- Gases are made up of particles (atoms or molecules) which are in constant random motion in straight lines.
- The particles behave as rigid spheres.
- Pressure is due to collisions between the particles and the walls of the container.
- All collisions, both between the particles themselves, and between the particles and the walls of the container, are perfectly elastic. (That means that there is no loss of kinetic energy during the collision.)
- The temperature of the gas is proportional to the average kinetic energy of the molecules.
An ideal gas is a further simplified model of a gas. It makes the following additional assumptions about gases:
- The particles are point masses (ie they occupy zero volume)
This is a good approximation until the pressures are very large, or the temperatures are approaching 0 K (absolute zero), as the volume of the particles can be considered to be insignificant compared to the larger volumes of space between particles.
- There are no intermolecular forces between gas particles.
This is a good approximation as long as high pressures and/or low temperatures are again avoided.
Pressure on the walls of the container is caused by collisions of the particles with the wall as each collision exerts a force on the wall. It can be understood that particles colliding with the walls at a higher rate (number per second) or with higher velocity will create a higher pressure.
Ideal Gas Law
Boyle’s Law, that we have just looked at, can be derived from the ideal gas law. The Ideal Gas Law is an equation that relates many of the properties of an ideal gas. The Ideal Gas Law is easily expressed as an equation:
| PV = nRT |
Where:
P = pressure of the gas (Pa)
V = volume of the gas (m³)
n = number of gas atoms present (mol)
R = Ideal Gas Constant
T = absolute temperature of the gas (K)
R has the value 8.31446261815324 J K−1 mol−1.
(recall that 1 mol = 6.02214076×1023)
Boyle’s Law
Boyle’s Law can be defined:
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The absolute pressure exerted by a given mass of an ideal gas is inversely proportional to the volume it occupies if the temperature and amount of gas remain unchanged within a closed system |
In equation form we usually write this as:
| P1V1 = P2V2 |
Or,
| PV = k1 |
We can easily determine that the constant k1 = nRT.
Charles’s Law
Charles’s Law describes how the volume of a gas behave when. heated when the pressure is kept constant. (eg. during heating whilst kept at atmospheric pressure.)
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When the pressure on a sample of a dry gas is held constant, the absolute temperature and the volume will be in direct proportion. |
In equation form we usually write this as:
| V ∝ T |
Or,
| V = k2T |
We can easily determine that the constant k2 = nR/P.
Gay-Lussac’s Law
This relates the pressure to the absolute temperature for a fixed mass of gas contained in a fixed volume.
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For a given mass and constant volume of an ideal gas, the pressure exerted on the sides of its container is directly proportional to its absolute temperature.. |
In equation form we usually write this as:
| P = k3T |
We can easily determine that the constant k3 = nR/V.
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