Thermal

• The internal energy of a body is equal to the sum of all the kinetic energies and potential energies of all its particles
• Kinetic and potential energies of a body are randomly distributed
• Internal energy of a system can be increased in two ways:

  • Do work on the system to transfer energy to it (e.g. moving its particles/changing its shape)
  • Increase the temperature of the system
• When the state of a substance is changed, its internal energy also changes because the potential energy of the system changes, while the kinetic energy of the system is kept constant
• Specific heat capacity of a substance is 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 of a substance is the amount of energy required to change the state of 1 kg of material, without changing its temperature
• There are two types of specific latent heat: specific latent heat of fusion (when solid changes to liquid) and specific latent heat of vaporisation (when liquid changes to gas)
• Gas laws describe the experimental relationship 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
• The Pressure Law: When volume is constant, pressure is directly proportional to absolute temperature
• The absolute scale of temperature is the kelvin scale, where a change of 1 K is equal to a change of 1°C
• Absolute zero (-273°C), also known as 0 K, is the lowest possible temperature where particles have no kinetic energy and the volume and pressure of a gas are zero
• Ideal gas equation: PV = nRT, where R is the molar gas constant (8.31 J mol^-1 K^-1)
• 1 mole of a substance is equal to 6.02 x 10^23 atoms/molecules
• Work done on a gas to change its volume at constant pressure can be calculated using the formula: Work done = pressure x change in volume
• Work done at constant pressure can be calculated using the formula: W = pΔV, where p is the pressure and ΔV is the change in volume
• Work done is especially useful when working with a graph of pressure against volume, as it is simply the area under the graph
• Brownian motion contributed to the evidence for the existence of atoms and molecules
• Brownian motion is the random motion of larger particles in a fluid caused by collisions with surrounding particles
• Boyle’s Law states that pressure is inversely proportional to volume at constant temperature
• Charles’s Law states that volume is directly proportional to temperature at constant pressure
• Pressure Law states that pressure is directly proportional to temperature at constant volume
• 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 equation relates several features of a fixed mass of gas, including its pressure, volume, and mean kinetic energy
• Assumptions of the kinetic theory model:

  • No intermolecular forces act on the molecules
  • The duration of collisions is negligible compared 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
• 6. Considering all directions the molecules will be moving in, the speed can be calculated using Pythagoras’ theorem: c^2 = u^2 + v^2 + w^2
• Derivation of the kinetic theory model:

  1. Consider a cube full of gas molecules with side lengths l, where one molecule with mass m is travelling towards the right-most wall with velocity u

  2. The time between collisions is t = 2l/u

  3. Impulse is found by dividing impulse by the area of one wall to find pressure: P = Vmu^2

  4. Total pressure of the gas is the sum of all individual pressures caused by each molecule: P = Vm(u1^2 + u2^2 + ... + un^2)

  5. Mean square speed is defined as u^2 = VNmμ^2
• An ideal gas follows the gas laws perfectly, meaning there are no other interactions other than perfectly elastic collisions between gas molecules
• The internal energy of an ideal gas is equal to the sum of the kinetic energies of all its particles
• Equations to find the kinetic energy of a single gas molecule can be used to find the internal energy of an ideal gas
• The kinetic energy of a gas molecule is directly proportional to temperature in Kelvin
• Example question: Find the sum of the kinetic energies of all oxygen molecules in a bottle containing 128g of oxygen at 330K (Molecular mass of oxygen gas = 32g)

  • Number of moles = 128/32 = 4
  • Number of molecules = 4 x 6.022 x 10^23 = 2.408 x 10^24
  • Kinetic energy of a single molecule = 6.831 x 10^-21 J
  • Sum of kinetic energies = 6.4501 J
• Knowledge and understanding of gases changes over time based on experimental evidence gathered by the scientific community