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THERMAL PROCESSES

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

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THERMAL PROCESSES

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  1. THERMALPROCESSES • 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

  2. THERMALPROCESSES • 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.

  3. 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

  4. 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.

  5. 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.

  6. 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,

  7. 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

  8. 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)

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