Paper 2 Thermal Physics

• Internal energy


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


  • Randomly distributed kinetic and potential energies of particles
• 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, volume, and temperature 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


  Absolute scale of temperature, 1 K = 1°C

  
• Absolute zero


  Lowest possible temperature, -273°C or 0 K, where particles have no kinetic energy and volume and pressure of a gas are zero
• Mole


  6.02 x 10^23 atoms/molecules
• Molar mass


  Mass (in grams) of one mole of a substance, approximately equal to sum of nucleons in a molecule
• Brownian motion is the random motion of larger particles in a fluid caused by collisions with surrounding particles, and contributed to the evidence for the existence of atoms and molecules
• Explaining gas laws using simple molecular model

  1. Boyle's law: Increasing volume decreases pressure due to less frequent collisions

  2. Charles's law: Increasing temperature increases volume due to increased kinetic energy of molecules

  
• Calculating work done


  1. W = pΔV

  2. Where p is pressure and ΔV is change in volume

  
• Work done is 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 volume increases, pressure decreases

  
• Charles's law


  1. Volume is directly proportional to temperature at constant pressure

  2. If temperature increases, volume increases

  
• Pressure law


  1. Pressure is directly proportional to temperature at constant volume

  2. If temperature increases, pressure increases

  
• 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 based on theory rather than empirical evidence
• 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 length l, full of gas molecules

  2. One molecule has mass m and velocity u, collides elastically with wall

  3. Change in momentum of molecule is 2mu

  4. Time between collisions is 2l/u

  5. Impulse (rate of change of momentum) is mu/l

  6. Pressure is impulse divided by area of wall, which is mu^2/V

  7. Total pressure is sum of pressures from all molecules

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

  9. Use Pythagoras' theorem to find speed in 3D, c^2 = u^2 + v^2 + w^2

  10. Assume mean square speed is the same in each direction, u^2 = v^2 = w^2

  11. Therefore c^2 = 3u^2 and p = (1/3)Nmc^2/V
• Ideal gas


  Follows the gas laws perfectly, with no other interaction other than perfectly elastic collisions between molecules, and no potential energy
• Internal energy of an ideal gas

  Equal to the sum of the kinetic energies of all its particles
• Calculating kinetic energy of a gas molecule


  Kinetic energy = (1/2)mc^2 = (3/2)kT = (2/3)NAkT

  
• Knowledge and understanding of gases has changed over time as new experimental evidence is gathered by the scientific community