# Chapter 13- Matter: Very Simple

A summary of Advancing Physics chapter 13

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• Created by: R_Hall
• Created on: 03-03-14 20:37

## Ideal Gases

• Absolute zero- the lowest possible temperature. 0K or -273°C
• To convert from °C to K, add 273
• Ideal gases obey the three following laws-
• Boyle's Law- at a constant temperature, the pressure of a gas is inversely proportional to the volume. pV = constant
• Charles' Law- at a constant pressure, the volume of a gas is directly proportional to its absolute temperature. V/T = constant
• The Pressure Law- at a constant volume, the pressure of a gas is directly proportional to its absolute temperature. p/T = constant
• Combining all three gas laws with the number of moles and the molar gas constant gives the ideal gas equation, pV = nRT
• One mole of gas contains 6.02 x 1023 particles. This is Avogadro's constant, NA.
• Boltzmann's constant, k, is the gas constant for one particle of gas, whereas NA is for one mole of gas
• Equation of state = pV = NkT
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## The Pressure of an Ideal Gas

• Particle velocity is proportional to pressure. The faster the particle, the greater the momentum and the greater the number of collisions. As pressure = force/area, pressure will increase
• The number of particles is proportional to pressure. Each particle exerts a force, so the greater the number of particles the greater the force, and the greater the pressure
• The volume of a box is inversely proportional to the pressure. In a small volume, particles have less space to travel in, so collisions will be more frequent. The area is smaller, so pressure is higher
• Particles travel in random directions at different velocities. You can estimate a third of the particles are travelling in one dimension at any time
• Simplifying assumptions for kinetic theory- 1. The gas contains a large no. of particles 2. The particles move rapidly and randomly 3. The motion follows Newton's laws 4. All collisions are perfectly elastic 5. There are no attractive forces between particles 6. Any forces acting are instantaneous 7. Particles have a negligible volume compared with the container volume
• Each particle goes on a random walk, moving N steps. The particle changes direction each time it collides. Average distance moved is proportional to √N
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## Internal Energy and Temperature

• If body A and B are in thermal equilibrium with C, then A and B must be in equilibrium with each other. Thermal energy flows between the bodies until the reach thermal equilibrium, and all have the same temperature. Energy is transferred from hot to cold
• Specific thermal capacity is the amount of energy needed to raise the temperature of 1kg of a substance by 1K
• Energy change = mass x specific thermal capacity x change in temperature
• Speed distribution of gas particles depends on temperature. As temperature of a gas increases, average particle speed increases, maximum particle speed increases and the distribution curve becomes more spread out
• Energy is transferred between particles when they collide. However, collisions do not alter the total energy in the system, as in each collision one particle gains energy the other particle loses. The average speed will stay the same (providing temperature is constant)
• Internal energy is the sum of kinetic and potential energy of the particles in a system
• Average kinetic energy is proportional to absolute temperature
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