PV = NKT. k = Boltzmann Constant = 1.38 x 10^-23

P = pressure

V = volume

T = temperature

N = n*Na = number of molecules

Na = Avogadro’s constant

n = number of moles

Ideal Gas Law = PV = nRT

R = universal gas constant = 8.31

Thermal Energy: Energy stored within the individual molecule of a gas

Molecules can take up energy by:

• Moving faster

• Rotating faster

Degrees of Freedom (f): The number of independent ways a molecule can store energy.

Monotomic gas (ex: Ar) : f = 3

Diatomic gas (ex: O2) : f = 5

solids : f = 6

Each f contributes an amount (1/2)*k*T to the energy of a molecule.

so thermal energy (Utherm) = N * f *(1/2) k T

Vibrational degrees of freedom only participate at high temperatures:

• from 200 - 1000K rotations are considered

• from 1500 K vibrations are considered

Internal Energy (U): total energy stored in molecules

Potential Energy (Upot) : The energy in the interaction between molecules

U = Utherm + Upot = 3NkT

Compressing a system leads to a decrease in Upot

For ideal gases, Upot is negligible compared to the Utherm so,

U = Utherm = Nf(1/2)kT = nf(1/2)RT

For an ideal gas, this energy does not depend on the volume!! It only depends on the number of particles and the temperature.