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Additional Reading Statistical Mechanics - Chapter 4

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Mathematics Flashcards on Additional Reading Statistical Mechanics - Chapter 4, created by Lauren Pollock on 18/05/2017.
Lauren Pollock
Flashcards by Lauren Pollock, updated more than 1 year ago
Lauren Pollock
Created by Lauren Pollock about 8 years ago
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Question Answer
First Order Phase Transition The 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.
Second Order Phase Transition The first derivative of the Gibbs potential is continuous but the second derivative is discontinuous.
Vapour Pressure The pressure at which gas and liquid coexist at thermal equilibrium during the transition region
Latent Heat The 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)
Critical Point The point at which gas and liquid have equal density and specific entropy. Phase transition becomes 2nd order.
Triple Point The 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.
Critical Isotherm A constant temperature line on the PT diagram which has an inflection point at the critical point.
Clayperon Equation (∂Δg/∂T)_P * (∂T/∂P)_Δg * (∂P/∂Δg)_T = -1 In equilibrium Δg = 0 dP/dt = l/(TΔV)
Intermolecular Potential Energy Dependent 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
Van der Waals Equation of State 1. 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
Virial Expansion Expresses 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)
Van der Waals Isotherms At T=T_c, the roots merge. At T<T_c 3 real roots. At T>T_c, one real root and one complex conjugate pair.
Isothermal Compressibility Describes the behaviour of a solid or liquid when the external pressure is changed β_T = -1/V (∂V/∂P)_T
Metastable The 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
Cavitation Formation of vapour cavities in a liquid (bubbles).
Spinodal Decomposition Mechanism for the rapid separation of 2 phases into two coexisting phases - it is local and spontaneous
Nucleation A physical process in which the change of state occurs around certain focal points known as nuclei
Condition for phase coexistence In 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.
Maxwell Construction VdW 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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