Energy in Thermal Physics (Lecture 1)

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==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

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^^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

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^^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.

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