THERMAL PROCESSES

• When a thermal variable changes there is a thermal process occurring.

• Reservoir = does not change during a thermal process.

• P V diagram T=constant isothermal• P T diagram V=constant isochoric• V T diagram P=constant isobaric• Any diagram ΔE=constant adiabatic

THERMAL PROCESSES

• Real Gases deviate from the ideal gas law• The P vs T, P vs V and V vs T diagrams

for real gases must also incorporate phase changes. These are called phase diagrams and the boundary across a solid liquid, or solid vapor or liquid vapor indicates where the phase changes these are not transformations.

REAL GASES

• What equation is used for real gases?• van der Waals equation • [ p + a(n/V)2 ] [V/n –b] = RT• a = f(intermolecular forces)• b = f(finite molecular size) • n = number of moles • Another form is: p = RT/(V/n –b) – a/(V/n)2

REAL GASES

• Two other equations used for real gases: Redlich-Kwong equation p = RT/(V/n –b) - a/{V/n(V/n + b)T1/2} where a and b are different constants.Beattie-Bridgeman equation

p = RT/(V/n) + β/(V/n)2 +γ/(V/n)3 +δ/(V/n)4

β, γ and δ are determined by five other experimental constants.

Blackbody Radiation

• When charged particles accelerate they produce electromagnetic waves. This is the condition of an body above absolute zero and the waves that are generated is called Black Body Radiation.

• As T increases the radiated energy becomes more intense and the average energy increases. Since the particles which generate the waves have a distribution of velocities, so does the radiation.

Blackbody Radiation

• The distribution of radiated energy per unit volume with a frequency between f and f+Δf is given by Planck’s Formula:

• u(f,T) Δf = (8πh/c3) f3Δf /(ehf/kT -1) where h= 6.625 x 10-34 Js c = 3 x 108 m/s Implies E = hf is a quantized energy photon If one considers the total power radiated

from a hole in a hot enclosure by integrating u(f,T) over all frequencies,

Blackbody Radiation• then this produces the Stephan-Boltzmann

formula.• R(T) = σ T4 (Watts/m2) where σ = 2 π5 k4/(15 c2 h3) having a value of 5.67 x 10-8 W/(m2 K4)To obtain the total radiated energy one

integrates over the surface. If R =constant then, E(T) = R *A

Blackbody Radiation

At very low energies compared to kT u(f,T) = 8πf2kT/c3

At very high energies compared to kT u(f,T) =(8πhf3/c3) e-hf/kT

(Raleigh-Jeans Catastrophe)If expressed as u(λ,T) f = c/λ u(λ,T) = (8πhc)/ λ5(ehf/kT -1)