Thermal

• Internal energy


  The sum of all of the kinetic energies and potential energies of all its particles
• Internal energy


  • Kinetic and potential energies of a body are randomly distributed
• Increasing internal energy of a system

  1. Do work on the system to transfer energy to it

  2. Increase the temperature of the system
• When the state of a substance is changed

  Its internal energy also changes
• The temperature increases up until 100°C, after which the energy gained through heating the water is no longer used to increase the temperature (and therefore kinetic energy), but instead is used to break bonds between water molecules so it can change state to water vapour, and so the potential energy is increased
• Specific heat capacity


  The amount of energy required to increase the temperature of 1 kg of a substance by 1 °C/1 K, without changing its state
• Specific latent heat


  The amount of energy required to change the state of 1 kg of material, without changing its temperature
• Specific latent heat of fusion


  When solid changes to liquid
• Specific latent heat of vaporisation


  When liquid changes to gas
• Calculating time taken for water to reach 100°C in a kettle

  1. Find energy required using Q = mcΔθ

  2. Divide energy required by power to get time
• Calculating final temperature when ice cube melts in water

  1. Find energy required to change state of ice

  2. Set up simultaneous equations for energy transfer in ice and water to find final temperature
• Calculating increase in temperature of water flowing past an electric heater

  Use Q = mcΔθ with power of heater and mass flow rate of water
• Gas laws


  Experimental relationships between pressure (p), volume (V), and temperature (T) for a fixed mass of gas
• Boyle's Law


  When temperature is constant, pressure and volume are inversely proportional
• Charles' Law


  When pressure is constant, volume is directly proportional to absolute temperature
• Pressure Law


  When volume is constant, pressure is directly proportional to absolute temperature
• Kelvin scale


  The absolute scale of temperature, where 1 K = 1°C
• Absolute zero


  The lowest possible temperature, where particles have no kinetic energy and the volume and pressure of a gas are zero
• Mole


  Equal to 6.02 x 10^23 atoms/molecules
• Molar mass


  The mass (in grams) of one mole of a substance
• Brownian motion


  The random motion of larger particles in a fluid caused by collisions with surrounding particles
• Brownian motion


  Contributed to the evidence for the existence of atoms and molecules
• Simple molecular model


  Can be used to explain the gas laws
• Boyle's law explained by molecular model

  If volume increases, molecules move further apart so collisions are less frequent, therefore pressure decreases
• Charles' law explained by molecular model

  If temperature increases, molecules move faster so collisions are more frequent, therefore volume increases
• Work done is simply the area under the pressure-volume graph
• Brownian motion


  Random motion of larger particles in a fluid caused by collisions with surrounding particles
• Brownian motion contributed to the evidence for the existence of atoms and molecules
• Boyle's law


  1. Pressure is inversely proportional to volume at constant temperature

  2. If you increase the volume of a fixed mass of gas, its molecules will move further apart so collisions will be less frequent therefore pressure decreases
• Charles's law


  1. Volume is directly proportional to temperature at constant pressure

  2. When the temperature of a gas is increased, its molecules gain kinetic energy meaning they will move more quickly and because pressure is kept constant (therefore frequency of collisions is constant) the molecules move further apart and volume is increased
• Pressure Law


  1. Pressure is directly proportional to temperature at constant volume

  2. When the temperature of a gas is increased, its molecules gain kinetic energy meaning they will move more quickly, as volume is constant the frequency of collisions between molecules and their container increases and they collide at higher speeds therefore pressure is increased
• The gas laws are empirical in nature, meaning they are not based on theory but arose from observation and experimental evidence
• The kinetic theory model is the opposite of the gas laws and arose from only theory
• Assumptions of the kinetic theory model

  • No intermolecular forces act on the molecules
  • The duration of collisions is negligible in comparison to time between collisions
  • The motion of molecules is random, and they experience perfectly elastic collisions
  • The motion of the molecules follows Newton's laws
  • The molecules move in straight lines between collisions
• Derivation of the kinetic theory model equation


  1. Consider a cube with side lengths l, full of gas molecules

  2. One molecule has mass m and is travelling with velocity u towards the right-most wall

  3. Assuming elastic collision, the change in momentum is 2mu

  4. Time between collisions is t = 2l/u

  5. Impulse = force = 2mu/2l = mu^2/l

  6. Pressure = impulse/area = mu^2/l^3 = mu^2/V

  7. Total pressure is the sum of all individual pressures

  8. Define mean square speed u^2 and multiply by N particles

  9. Use Pythagoras' theorem to get c^2 = u^2 + v^2 + w^2, and assume u^2 = v^2 = w^2

  10. Substitute this into the pressure equation to get p = (1/3)Nmc^2/V
• Ideal gas


  Follows the gas laws perfectly, meaning there is no other interaction other than perfectly elastic collisions between the gas molecules, which shows that no intermolecular forces act between molecules
• An ideal gas has no potential energy, therefore its internal energy is equal to the sum of the kinetic energies of all of its particles
• Kinetic energy of a single gas molecule

  m(c_rms)^2/2 = (3/2)kT = (3/2)RT/N_A
• Example problem: Find the sum of the kinetic energies of all the oxygen molecules in a 128g bottle at 330K

  1. Number of moles = 128g / 32g/mol = 4 mol

  2. Number of molecules = 4 mol * 6.022 x 10^23 molecules/mol = 2.408 x 10^24 molecules

  3. Kinetic energy of a single molecule = (3/2)kT = 6.831 x 10^-21 J

  4. Sum of kinetic energies = 2.408 x 10^24 molecules * 6.831 x 10^-21 J/molecule = 16450 J
• Knowledge and understanding of gases has changed greatly over time, with the gas laws being empirical and the kinetic theory model being theoretical