Karteikarten
Physics of Matter Equations
Karten in diesem Stapel (58)
- 1Critical temperatureTemperature at which critical point occurs
T=deltaE/kb - 2Intermolecular potential per unit volumeU=1/2 p^2INTEGRAL(gV)
g is radial distribution function - 3FluxJ = 1/4 n
n number density - 4Pressure of a gas (think flux)P=1/3 nm
- 5Pressure difference in gasP=Po e^(-mgh/kbT)
- 6Maxwell-Boltzmann distribution function1/N dN/dc = 4pic^2 (m/2pikbT)^3/2 e^(-mc^2/2kbT)
- 7Most probable speed of a moleculec* = SQRT(2kbT/pim)
- 8Mean speed= SQRT(8kbT/pim)
- 9Root mean square speedSQRT() = SQRT(3kT/m)
- 10Mean free pathmfp=1/pio^2n
o diameter of molecule, radius of cylinder swept out by particle - 11Effusion relation pressure and temperatureP1/P2=SQRT(T2/T1)
- 12Fick's LawFor diffusion
J=-D dn/dz - 13Diffusion coefficientD= -mfp/3 dn/dz
- 14ViscosityVISC=1/3 m mfp n
n number of molecules - 15Thermal conductivityk = 1/3 n mfp (cv)
cv = heat capacity constant v - 16First law of thermodynamicsdeltaU = Q + W
- 17Work done on gas at constant pressureW = -P(Vf-Vi)
- 18Work done in a reversible isothermal expansionW=-NRTln(Vf/Vi)
- 19Heat capacity at constant VdQ/dT=dU/dT
- 20Heat capacity constant PdQ/dT
- 21EnthalpyH=U+PV
- 22Spacing between rotational energy levelse=hbar^2/4pi^2I
I moment of inertia - 23Relationship between cV and cPcP=Cv +(dU/dV +P)dV/dT
- 24Change in volume due to isobaric thermal expansivitydeltaV=B V delta T
- 25Change in volume due to isothermal compressibilityk+ - 1/V (dV/dP)
- 26Ratio of cP and cV-V/P dP/dV = gamma
- 27Relationship between P and V for adiabatic expansionP1V1^gamma = P2V2^gamma... etc
Gamma is the ratio of cP to cV - 28Cooling due to adiabatic expansionT2/T1 = (V1/V2)^gamma-1= (P2/P1)^((gamma - 1)/gamma)
- 29EntropydS=dQ/T = dH/T
- 302nd law of thermodynamicsdelta S(univ) >/ 0
- 31Gibb's Free EnergyG=H-TS
- 32Master EquationsdH=TdS+vdP
dG =VdP - SdT - 33Clapeyron EquationdP/dT = Svap-Ssol/Vvap-Vsol
- 34Clasius Clapeyron Equationln(P2/P1) = - deltaH/R (1/T2-1/T1)
- 35Latent heat of vaporisationL= deltaHvap
- 36Van der Waals equationP=RT/V-b - a/V^2
v = volume of one mole - 37b in Van der Waals Equationb=4Nav=2pi/3 Na o^3
v = volume of one molecule
o = diameter of one molecule - 38Missing neighbours of a molecule approaching a walln-no = - ano^2/kT
a = alpha = some constant - 39Critical temperature of liquidTc=8a/27Rb = 26 deltae/27k
a and b are constants from the Van der Waals equation n - 40Keesom interactionU = -2u1^2u2^2/3kT(4piEo)^2r^6
ui = dipole moment
r = distance between two charges in dipole - 41Induced dipole momentu = aE
a = alpha = polarizability - 42Lennard Jone's PotentialU = 4e((o/r)^12 - (o/r)^6)
o = distance at which U is zero
r = distance between particles - 43Surface free energyeNbrok/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 - 44Latent heat of vapourisationL = 1/2 qNae
q = number of near neighbours - 45Young's Equationgamma(sv) = gamma(sl) +gamma(l)costheta
found by decomposing the surface free energies at a contact angle between liquid and a solid - 46Pressure difference across curved interfaceP1=P2 = gamma(1/R1+1/R2)
- 47Bernoullis EquationP1/p1 +1/2 v1^2 +phi1 = P2/p2 +1/2 v2^2+phi2
p = density
phi = gz - 48Stoke's EquationsViscous force
F = 6pinRv
n = viscosity
R = radius - 49Reynolds NumberRe = pvR/n
n viscosity
p density
R radius - 50Ionic pair potentialU = 1.481e[+/- (o/r)+(o/r)^9]
- 51Packing FractionPF = NpVp/Vuc
- 52Plane spacingd = a/SQRT[h^2+k^2+l^2)]
h,k,l miller indices - 53Lattice energy of Van der Waal solidUt<2eNa[12(o/r1)^12 - 14.05(o/r1)^6]
- 54Ionic lattice energyUt=0.741eNa[6(o/r1)^9-1.75(o/r1)]
- 55Braggs Law Cubic System(sin0)^2 = lambda^2(h^2+k^2+l^2)/4a^2
- 56Einstein model for specific heatCv = 3R(0e/T)^2 e^(0e/T) / [(e^(0/T)-1)^2]
0e = hbarw/k - 57Debye frequencyw = k0/hbar
0 = debye temp - 58Young's Modulus72e/ro^3
e = strain
ro = distance
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- Physics of Matter equations
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- Lauren Clark
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