Karteikarten
Additional Reading Statistical Mechanics - Chapter 4
Karten in diesem Stapel (19)
- 1First Order Phase TransitionThe Gibbs potential is continuous from one phase to another but in a first order phase transition, the first derivatives of the Gibbs potential are discontinuous. This discontinuity originates from the difference in density and specific entropy between the two phases.
- 2Second Order Phase TransitionThe first derivative of the Gibbs potential is continuous but the second derivative is discontinuous.
- 3Vapour PressureThe pressure at which gas and liquid coexist at thermal equilibrium during the transition region
- 4Latent HeatThe energy released or absorbed during a constant temperature process. The heat released during a phase transition is due to the differing entropies of coexisting phases. When a unit amount of phase 1 is converted into phase 2, an amount of latent heat is liberated: l = T_0(s_2-s_1)
- 5Critical PointThe point at which gas and liquid have equal density and specific entropy. Phase transition becomes 2nd order.
- 6Triple PointThe line along which the gas, liquid and solid can all coexist projects onto the triple point in the PT diagram. The temperature at which all 3 phases can coexist in equilibrium.
- 7Critical IsothermA constant temperature line on the PT diagram which has an inflection point at the critical point.
- 8Clayperon Equation(∂Δg/∂T)_P * (∂T/∂P)_Δg * (∂P/∂Δg)_T = -1
In equilibrium Δg = 0
dP/dt = l/(TΔV) - 9Intermolecular Potential EnergyDependent on the magnitude of the intermolecular forces and the position the molecules have relative to each other at any instant of time.
1. Repulsive core - due to the electrostatic repulsion between electron clouds
2. Attractive tail - due to the mutual electrostatic polarisation - 10Van der Waals Equation of State1. Hard core replusion leads to V_eff = V-b
2. Reduction due to attraction of neighbouring molecules P =Pkinetic - a/V^2
(V - b)(P + a/V^2) = RT - 11Virial ExpansionExpresses the pressure of a many particle system in equilibrium as a power series in the number density.
PV/RT = 1 + 1/V(b - a/RT) - 12Van der Waals IsothermsAt T=T_c, the roots merge. At TT_c, one real root and one complex conjugate pair.
- 13Isothermal CompressibilityDescribes the behaviour of a solid or liquid when the external pressure is changed
β_T = -1/V (∂V/∂P)_T - 14MetastableThe stability of a dynamical system in a configuration other than the systems state of least energy (all state defining parameters reach and maintain stationary values).
Positive compressibility = Metastable
Negative compressibility = Unstable - 15CavitationFormation of vapour cavities in a liquid (bubbles).
- 16Spinodal DecompositionMechanism for the rapid separation of 2 phases into two coexisting phases - it is local and spontaneous
- 17NucleationA physical process in which the change of state occurs around certain focal points known as nuclei
- 18Condition for phase coexistenceIn a 1st order transition, coexisting phases have the same P and T. Therefore the condition for equilibrium is therefore that the total Gibbs potential be minimum.
G = g_1m_1 + g_2m+2
Condition for phase coexistence:
Δg = g_1 - g_2 = 0 - i.e. coexisting phases must have equal chemical potential. - 19Maxwell ConstructionVdW isotherm is a monotomic function of V for T>T_c. Below T_c, kink displaying negative compressibility - due to assumption density is uniform. 1st order transition actually involves break up in a mix of phase derivatives.
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- Mathematics Karteikarten am Additional Reading Statistical Mechanics - Chapter 4, erstellt von Lauren Pollock am 18/05/2017.
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- Lauren Pollock
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