notes

• 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

  change force on a sealed gas syringe, calculate pressure exerted and subtract from atmospheric pressure 101kPa

  
• Charles' Law


  When pressure is constant, volume is directly proportional to absolute temperature

  measure height of trapped air bubble in capillary tube when temperature is changed + tube is open at top therefore pressure is constant

  
• Pressure Law


  When volume is constant, pressure is directly proportional to absolute temperature

  change in temp of gas in flask in water bath, use pressure gauge

  
• Kelvin scale


  Absolute scale of temperature, 1 K = -273°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
• Molar mass


  Mass (in grams) of one mole of a substance, found from relative molecular mass
• Brownian motion is the random motion of larger particles in a fluid caused by collisions with surrounding particles, and can be observed through looking at smoke particles under a microscope
• Brownian motion contributed to the evidence for the existence of atoms and molecules
• Work done is simply the area under the graph of pressure against volume

  
• Brownian motion


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

  3. Assume it collides with the right-most wall elastically, its change in momentum is mu - (-mu) = 2mu

  4. Before this molecule can collide with this wall again it must travel a distance of 2l, therefore the 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 = Nmu^2/V

  8. Define mean square speed u^2 = (u^1)^2 + (u^2)^2 + ... + (u^n)^2 / N

  9. Use Pythagoras' theorem to find the speed the molecules will be travelling at: c^2 = u^2 + v^2 + w^2, where u, v, w are the components in x, y, z directions

  10. Assume mean square speed in each direction is the same, so u^2 = v^2 = w^2 and c^2 = 3u^2

  11. 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 question: Find the sum of the kinetic energies of all the oxygen molecules in a bottle containing 128 g of oxygen at 330 K

  1. Number of moles = 128 g / 32 g/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 = (3/2) * 1.38 x 10^-23 J/K * 330 K = 6.831 x 10^-21 J

  4. Sum of kinetic energies = 6.831 x 10^-21 J/molecule * 2.408 x 10^24 molecules = 16,450 J
• Knowledge and understanding of gases has changed greatly over time; the gas laws were discovered by a number of scientists and later explained by the development of the kinetic theory model, however this model wasn't accepted at first
• Knowledge and understanding of any scientific concept changes over time in accordance to the experimental evidence gathered by the scientific community
• Force field


  An area in which an object experiences a non-contact force
• Force fields


  • Can be represented as vectors, which describe the direction of the force that would be exerted on the object
  • Can be represented as diagrams containing field lines, the distance between field lines represents the strength of the force exerted by the field in that region

  
• Formation of force fields

  1. Interaction of masses

  2. Interaction of static charge

  3. Interaction of moving charges
• Types of force fields

  • Gravitational fields
  • Electric fields