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Zeroth Law: If system x = system y & system y = system z, then system x = system z. (Transitive)
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First Law: Internal energy(ΔU) of an isolated system is constant. No heat lost, only transferred.
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Second Law: The entropy of any isolated system always increases.
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Third Law: The entropy of a system approaches a constant value as the temperature approaches absolute zero.
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Cyclic Rule: (dP/dT)
v(dT/dV)p(dV/dP)T= -1 |
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Adiabatic: No transfer of heat or matter
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Diathermal: Heat allowed to transfer, no matter transfer. Can transfer energy in the form of work
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Enthalpy(ΔH): Amount of heat content used or released in a system at constant pressure
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Irreversible: A process that cannot return both the system and the surroundings to their original conditions.
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ΔU=m
s/Ms ΔUcomb+mH2O/MH2O Cv,m(H2O)ΔT+ΔTCcalorimeter |
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ΔHo=m
salt/Msalt ΔHosolution+mH2O/MH2O Cp,m(H2O)ΔT+ΔTCcalorimeter |
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S=k ln(W) W=#of states
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Efficiency = 1-|q
cd|/|qab| <1 |
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ΔHo
rt=ΔHo298+∫ΔCp(T) dT from 298 to T |
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ΔH
combustion = ΔUcombustion+Δ(PV) |
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For Solids & Liquids: ΔH~= ΔU
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Δs=-nRln(P
f/Pi)+∫nCpm/T dT for Pi to Pf |
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Δs=nRln(V
f/Vi)+∫nCvm/T dT for Vi to Vf |
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Isolated System: ΔS=q
p(1/T1 - 1/T2) |
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Isothermal, Ideal: ΔS=nRln(V
f/Vi) |
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ΔS
total=ΔS+ΔSsurroundings |
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ΔG=nRT Σ x
iln(xi) xi is mole fraction |
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ΔG = TΔS
total |
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General
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ΔU=q+w
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Constant Volume
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ΔU=C
vΔT = qv |
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Adiabatic, Reversible
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ΔU= w = n(C
pm-R)ΔT = nCvmΔT |
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Ideal
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ΔU=nC
vmΔT |
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General
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ΔH= ΔU+Δ(PV) = ΔU+nRΔT
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Constant Pressure
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ΔH= C
pΔT |
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Ideal
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ΔH = q
p |
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Constant Volume
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ΔH= nC
pmΔT + VΔP |
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Even More General
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dH= (dH/dP)
T dT + (dH/dT)P dP |
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Liquids & Solids
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(dH/dP)
T = V(1-Tβ) |
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Constant Pressure, closed system
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ΔH= (U
f+PfVf)-(Ui+PiVi) |
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Isobaric
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ΔH= n∫C
pm(T) dT = nCpmΔT |
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S
m(T)=Sm(0ok) +∫Cpm/T dT(solid 0-Tf) +ΔHfus/Tf + ∫Cpm/T dT(liquid Tf-Tb) +ΔHvap/Tb ∫Cpm/T dT(gas Tb-T) ` |
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For Ideal Gases: ΔS
m=Rln(Vf/Vi)=-Rln(Pf/Pi) |
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ΔG(T
2)/T2= ΔG(T1)/T1+ΔH(T1)(1/T2-1/T1) |
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Max Work: Reversible, adiabatic, isothermal
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Hess's Law: Total Enthalpy change is independent of # of steps(path-independent).
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ΔA = ΔU-TΔS = ΔH-nRT (Hemholtz)
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for ΔGo
r only include non-pure substances. |
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ΔG
R = ΔG°R+RT ln(QP) |
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ln(K
P) = -ΔG°R/RT |
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K
x=KP(P/P°)-ΔV |
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dA = 𝛾 dσ gamma is surface tension
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Work = 8pi𝛾r dr
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Force = 8pi𝛾r
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h(capillary rise/depression) = 2𝛾/𝞺gr
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𝓾
B=𝓾°B+RTln(𝛾[B]) gamma is activity coefficient |
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ΔG
R = ΔG°R-2.303vRT(pH) |
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q
x = kA(Tsi-Tso)/L |
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q''
x= -k dT/dx = qx/A |
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Ė
in+Ėg-Ėout = Ėinternal |
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q
12 = εσA(T14-T24) - Heat xchange via radiation b/t 2 surfaces |
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q''
s = h(Ts-T∞) - Newton's Law of Cooling |
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