Pressure, Volume and Temperature
Most of this chapter will require temperatures in kelvin. Kelvin = celsius + 273.
There are three gas laws which relate volume, pressure and temperature.
- Boyles law is that pressure and volume are inversly proportional
- Pressure law is that pressure is proportional to temperature
- Charles law is that volume is proportional to temperature
If you combine all these laws you get that pV = nRT where n is number of moles or pV =NkT where N is the number of particles. These rules work for low pressure and fairly high temperature.
- Velocity is proportional to pressure since the particles will have more momentum so more force and also will hit the wall more.
- The number of particles is proportional to the pressure since more particles means a higher force
- The volume is inversly proportional to the pressure since less volume means less space between collisions so an increased total force. Also area is smaller
Combing all this : pV = 1/3 Nmc^2 Pressure = F /A
The assuptions of a ideal gas are that
- The gas contains a large amount of particles
- The particles move rapidly and randomly
- The particles follow newtons laws
- Collisions are perfectly elastic
- There are no attractive forces between particles
- Any forces that acts during collisions are instantaneous
- Particles have negligible volume compared with the volume of the container
The motion of a particle is a random walk. It will move √N steps in random directions since it will collide with other particles.
Specific thermal capacity
The specific heat capactity of a particle is the amount of energy needed to raise the temperature of 1kg of the substance by 1K. It can be found using: ΔE = mcΔθ
In a gas, not all particles have the same speed. They have a speed distribution. As the temperature of the gas increases the average particle speed increases and the maximum particle speed increases. Also the distribution curve becomes more spread out.
Energy is transfered between particles through collisions. Some particles will gain speed, and others will slow down. Between collision particles travel at constant speeds. The total energy of the system does not change and so the average speed will stay the same as long as the temperature stays constant.
The internal energy = KE + PE
The average kinetic energy of an individual particle = 1/2mc^2
1/2mc^2 = 3/2 nRT / N
So a rise in temperature will cause a increase in KE and so a higher internal energy
The average thermal energy per particle is roughly = kT
The energy needed to break the bonds in a substance is called the activation energy. When the ratio E/kT is big enough (Around 15-30) the process will happen at a steady rate and some particles must have 15-30 times the average energy. If the ratio is too high then nothing happens.
If the fraction of particles with extra energy E is represented as f then the fraction of particles with 2E is f^2.
The Boltzmann Factor
The boltzmann factor, e^-E/kT , gives the ratio of the number of particles in energy states E joules apart.
The temperature changes the boltzmann distribution. Lower temperatures mean the boltzmann factor is very low.