Thermodynamics: Ideal Gases

Ideal Gases

Key Equations and Concepts

A gas is considered ‘ideal’ if it follows the equation pV = nRT where p is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant and T is the temperature in kelvins.
Absolute zero is the theoretical point at which a substance would have zero thermal energy. It’s equivalent to -273.15 degrees Celsius.
The concept of the mole links the macroscopic world of bulk materials to the microscopic world of atoms and molecules. One mole of a substance contains Avogadro’s number of particles, which is approximately 6.022 x 10^23.
Molar mass is the mass of one mole of a substance, usually measured in grams per mole (g/mol).
Kelvin (K) is the unit for absolute temperature in the ideal gas law, with 0K being absolute zero.

Specific Heat Capacity and Latent Heat

Specific heat capacity (c) is the energy required to raise 1 kg of a substance by 1 degree Celsius. It’s measured in J kg^-1 °C^-1.
Latent heat (L) is the energy absorbed or released by a substance during a phase change. The latent heat of fusion (L_f) is the energy required for a substance to melt while the latent heat of vaporisation (L_v) is required for it to vaporise. Both are measured in J kg^-1.

Gas Laws

Boyle’s Law states that for a fixed amount of gas at a constant temperature, the product of pressure and volume (pV) is constant.
Charles’s Law states that for a fixed amount of gas at constant pressure, the volume is directly proportional to its absolute temperature (V/T = constant).
Pressure Law states that for a fixed volume of gas, the pressure is directly proportional to its absolute temperature (p/T = constant).

Kinetic Theory of Gases

The kinetic theory of gases assumes that gas molecules are very small compared to the distances between them and that they are in constant random motion.
Mean square speed is the square root of the average of the squares of the velocities of the molecules in a gas.
Root mean square speed (u_rms) is the square root of the mean square speed and is a way to determine an ‘average’ speed for gas particles at a given temperature.
The Maxwell-Boltzmann distribution describes the spread of speeds of particles in a gas at a certain temperature.

Thermodynamic Processes

Isothermal processes occur at constant temperature.
Adiabatic processes occur without any heat transfer into or out of the system.
Isochoric processes occur at constant volume.
Isobaric processes occur at constant pressure.