Thermal Physics & Ideal Gases

• Thermal equilibrium


  A state where there is no net flow of thermal energy between objects involved, i.e., the objects are at the same temperature
• Celsius scale


  Relies on the melting and boiling points of water under atmospheric pressure
• Thermodynamic scale


  Measured in kelvin, uses the triple point of water (273.16K) and absolute zero
• T (˚K) = T (˚C) + 273
• Solids


  Have tightly packed atoms, kept together by strong electrostatic forces of attraction; they have kinetic energy which allows them to vibrate in place
• Liquids


  Have a greater mean separation than solids but are still close together; they have more kinetic energy than solids which means they can change position and flow past each other
• Gases


  Have molecules that are far apart, with more kinetic energy than those in liquids; they are free to move past each other and collide elastically, moving in random directions with random speeds
• Brownian motion


  Where molecules of a gas travel in random directions with random velocities
• Brownian motion can be seen by looking at smoke particles in the air, which are visible under a microscope and shows random motion because it collides with the air molecules
• Internal energy


  Sum of the kinetic and potential energies in a substance
• When a substance is heated

  The kinetic energy increases but the potential energy remains the same
• When a substance changes state

  Potential energy increases but the kinetic energy remains the same
• Temperature remains the same when the substance changes state as the thermal energy goes to breaking the electrostatic forces
• Absolute zero is at 0˚K, the temperature at which the particles have no kinetic energy/minimum internal energy; they stop moving completely
• Specific heat capacity


  Energy required per unit mass to increase the temperature by 1˚K
• E = mc∆ø
• Specific latent heat of fusion

  The energy required for 1kg of substance to change state from solid to liquid
• Specific latent heat of vaporisation

  The energy required for 1kg of substance to change state from liquid to gas
• E = ml
• Amount of substance


  Measured in moles
• One mole has 6.02 x 10^23 particles (Avogadro’s constant)
• n = m / M where n = number of moles, m = mass, M = number of molecules
• Kinetic theory of gases


  Used to describe how ideal gases behave
• Assumptions about ideal gases

  • There are a large number of particles
  • Volume of the gas atoms are negligible compared to the large volume
  • Collisions are perfectly elastic
  • Time taken is negligible
  • Electrostatic forces are negligible
• Collisions inside a container are perfectly elastic so there is a change in momentum which leads to an increase in force
• Using Newton's third law, an atom exerts an equal and opposite force on the wall
• Total pressure


  The total force of each atom of gas with the container’s walls and the area of the wall
• Boyle’s law


  For a fixed mass at a constant temperature, pressure is inversely proportional to the volume
• Charles’ law


  For a fixed mass of gas at a constant pressure, the volume is directly proportional to temperature
• pV = nRT where n = number of moles, R = ideal gas constant
• Experiment to determine absolute zero

  1. Place a sealed container of air connected to a pressure gauge in a water bath

  2. Vary the temperature and record both the pressure and temperature

  3. Plot a graph of pressure against temperature

  4. Plot a line of best fit

  5. Extrapolate the graph until pressure = 0, and this is equal to absolute 0
• Root mean squared


  Related to the mean kinetic energy of a gas and the pressure
• Root mean squared is found by summing all of the squares of the velocities and dividing by the number of molecules and the square root of this value
• The root mean squared can be used to find pressure
• pV = 1/3 Nmc^2 where N = number of molecules, m = mass of a single particle, c = root mean squared
• Maxwell Boltzmann distribution


  Shows the number of molecules with each speed
• The area under the distribution represents the total number of molecules
• As the temperature increases

  The peak shifts to a higher speed and the distribution becomes more spread out
• Boltzmann constant (k)


  k = R / Na
• Boltzmann constant can be used to derive pV = NkT