Physics of Matter Equations

Pregunta	Respuesta
Critical temperature	Temperature at which critical point occurs T=deltaE/kb
Intermolecular potential per unit volume	U=1/2 p^2INTEGRAL(gV) g is radial distribution function
Flux	J = 1/4 n <c> n number density
Pressure of a gas (think flux)	P=1/3 nm <c^2>
Pressure difference in gas	P=Po e^(-mgh/kbT)
Maxwell-Boltzmann distribution function	1/N dN/dc = 4pic^2 (m/2pikbT)^3/2 e^(-mc^2/2kbT)
Most probable speed of a molecule	c* = SQRT(2kbT/pim)
Mean speed	<c> = SQRT(8kbT/pim)
Root mean square speed	SQRT(<c^2>) = SQRT(3kT/m)
Mean free path	mfp=1/pio^2n o diameter of molecule, radius of cylinder swept out by particle
Effusion relation pressure and temperature	P1/P2=SQRT(T2/T1)
Fick's Law	For diffusion J=-D dn/dz
Diffusion coefficient	D= -mfp/3 <c> dn/dz
Viscosity	VISC=1/3 m mfp n <c> n number of molecules
Thermal conductivity	k = 1/3 n mfp (cv) cv = heat capacity constant v
First law of thermodynamics	deltaU = Q + W
Work done on gas at constant pressure	W = -P(Vf-Vi)
Work done in a reversible isothermal expansion	W=-NRTln(Vf/Vi)
Heat capacity at constant V	dQ/dT=dU/dT
Heat capacity constant P	dQ/dT
Enthalpy	H=U+PV
Spacing between rotational energy levels	e=hbar^2/4pi^2I I moment of inertia
Relationship between cV and cP	cP=Cv +(dU/dV +P)dV/dT
Change in volume due to isobaric thermal expansivity	deltaV=B V delta T
Change in volume due to isothermal compressibility	k+ - 1/V (dV/dP)
Ratio of cP and cV	-V/P dP/dV = gamma
Relationship between P and V for adiabatic expansion	P1V1^gamma = P2V2^gamma... etc Gamma is the ratio of cP to cV
Cooling due to adiabatic expansion	T2/T1 = (V1/V2)^gamma-1= (P2/P1)^((gamma - 1)/gamma)
Entropy	dS=dQ/T = dH/T
2nd law of thermodynamics	delta S(univ) >/ 0
Gibb's Free Energy	G=H-TS
Master Equations	dH=TdS+vdP dG =VdP - SdT
Clapeyron Equation	dP/dT = Svap-Ssol/Vvap-Vsol
Clasius Clapeyron Equation	ln(P2/P1) = - deltaH/R (1/T2-1/T1)
Latent heat of vaporisation	L= deltaHvap
Van der Waals equation	P=RT/V-b - a/V^2 v = volume of one mole
b in Van der Waals Equation	b=4Nav=2pi/3 Na o^3 v = volume of one molecule o = diameter of one molecule
Missing neighbours of a molecule approaching a wall	n-no = - ano^2/kT a = alpha = some constant
Critical temperature of liquid	Tc=8a/27Rb = 26 deltae/27k a and b are constants from the Van der Waals equation n
Keesom interaction	U = -2u1^2u2^2/3kT(4piEo)^2r^6 ui = dipole moment r = distance between two charges in dipole
Induced dipole moment	u = aE a = alpha = polarizability
Lennard Jone's Potential	U = 4e((o/r)^12 - (o/r)^6) o = distance at which U is zero r = distance between particles
Surface free energy	eNbrok/2ro^2 = NbrokL/qNa(pNa/M)^2/3 ro = average seperation Nbrok = number of neighbours lost e = depth of Lennard Jones potential L = latent heat q = number of nearest neighbours
Latent heat of vapourisation	L = 1/2 qNae q = number of near neighbours
Young's Equation	gamma(sv) = gamma(sl) +gamma(l)costheta found by decomposing the surface free energies at a contact angle between liquid and a solid
Pressure difference across curved interface	P1=P2 = gamma(1/R1+1/R2)
Bernoullis Equation	P1/p1 +1/2 v1^2 +phi1 = P2/p2 +1/2 v2^2+phi2 p = density phi = gz
Stoke's Equations	Viscous force F = 6pinRv n = viscosity R = radius
Reynolds Number	Re = pvR/n n viscosity p density R radius
Ionic pair potential	U = 1.481e[+/- (o/r)+(o/r)^9]
Packing Fraction	PF = NpVp/Vuc
Plane spacing	d = a/SQRT[h^2+k^2+l^2)] h,k,l miller indices
Lattice energy of Van der Waal solid	Ut<2eNa[12(o/r1)^12 - 14.05(o/r1)^6]
Ionic lattice energy	Ut=0.741eNa[6(o/r1)^9-1.75(o/r1)]
Braggs Law Cubic System	(sin0)^2 = lambda^2(h^2+k^2+l^2)/4a^2
Einstein model for specific heat	Cv = 3R(0e/T)^2 e^(0e/T) / [(e^(0/T)-1)^2] 0e = hbarw/k
Debye frequency	w = k0/hbar 0 = debye temp
Young's Modulus	72e/ro^3 e = strain ro = distance

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	Creado por Lauren Clark hace alrededor de 9 años