Notes

Thermal Physics

Thermal energy transfer
The internal energy of a body is equal to the sum of all of the kinetic energies and potential
energies of all its particles.
The 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, this is because the
potential energy of the system changes, while the kinetic energy of the system is kept
constant.

Equations
Specific Heat Capacity: Where Q is energy required, m is the mass, c is the specific
heat capacity, and is the change in temperature.
The 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 heat capacity of water = 4200 J/kg°C )

Specific Latent Heat: Where Q is energy required and l is the specific latent heat.
(specific latent heat of fusion of ice = 334 J/kg)
The 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:
the specific latent heat of fusion (when solid changes to liquid) and specific latent heat of
vaporisation (when liquid changes to gas).

Ideal Gases
-Boyle’s Law -When temperature is constant, pressure and
volume are inversely proportional (PV=K)
-Charles’ Law -When pressure is constant, volume is directly
proportional to absolute temperature (V/T=K)
-The Pressure Law -When volume is constant, pressure is
directly proportional to absolute temperature (P/T=K)
Celsius to Kelvin: K = C + 273
Absolute zero (- 273°C ), also known as 0 K, is the lowest possible temperature, and is the
temperature at which particles have no kinetic energy and the volume and pressure of a gas are
zero.
pV= nRT , which is the ideal gas equation.
where n is the number of moles of gas, and 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, so you can convert between the
number of moles (n) and the number of molecules (N) by multiplying the number of moles by 6.02 x10^23
, which is defined as the Avogadro constant
pv=nkt ( k= boltzman constant)
Molar mass is the mass (in grams) of one mole of a substance and can be found by finding the
relative molecular mass, which is (approximately) equal to the sum of the nucleons in a molecule
of the substance.
Work done = pΔV
Where p is the pressure and Δv is the change in volume.

Molecular kinetic theory model
You can use a simple molecular model to explain each of the gas laws:
- Boyle’s law - Pressure is inversely proportional to volume at constant temperature
E.g 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 - Volume is directly proportional to temperature at constant pressure
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 - Pressure is directly proportional to temperature at constant volume
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 kinetic theory model equation relates several features of a fixed mass of gas, including its
pressure, volume and mean kinetic energy. There are several underlying assumptions, which lead
to the derivation of this equation:
Assumptions -
- No intermolecular forces act on the molecules
- The duration of collisions is negligible in comparison to time between collisions
- The motion of molecules in random, and they experience perfectly elastic collisions
- The motion of the molecules follows Newton’s laws
- The molecules move in straight lines between collisions

An ideal gas follows the gas laws perfectly, meaning that there is no other interaction other than
perfectly elastic collisions between the gas molecules, which shows that no intermolecular
forces act between molecules. As potential energy is associated with intermolecular forces, 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.