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313 Exam 3 Cheat Sheet by

Laws

Zeroth Law: If system x = system y & system y = system z, then system x = system z. (Trans­itive)
First Law: Internal energy(ΔU) of an isolated system is constant. No heat lost, only transf­erred.
Second Law: The entropy of any isolated system always increases.
Third Law: The entropy of a system approaches a constant value as the temper­ature approaches absolute zero.
Cyclic Rule: (dP/dT)v(dT/dV)p(dV/dP)T= -1

Defini­tions

Adiabatic: No transfer of heat or matter
Diathe­rmal: Heat allowed to transfer, no matter transfer. Can transfer energy in the form of work
Enthal­py(ΔH): Amount of heat content used or released in a system at constant pressure
Irreve­rsible: A process that cannot return both the system and the surrou­ndings to their original condit­ions.

Exam 2

ΔU=ms/Ms ΔUcomb+mH2O/MH2O Cv,m(H2O)Δ­T+ΔTCcalori­meter
ΔHo=msalt/Msalt ΔHosolution+mH2O/MH2O Cp,m(H2O)Δ­T+ΔTCcalori­meter
S=k ln(W) W=#of states
Efficiency = 1-|qcd|/|qab| <1
ΔHort=ΔHo298+∫ΔCp(T) dT from 298 to T
ΔHcombustion = ΔUcombustion+Δ(PV)
For Solids & Liquids: ΔH~= ΔU
Δs=-nRln(Pf/Pi)+∫nCpm/T dT for Pi to Pf
Δs=nRln(Vf/Vi)+∫nCvm/T dT for Vi to Vf
Isolated System: ΔS=qp(1/T1 - 1/T2)
Isothe­rmal, Ideal: ΔS=nRln(Vf/Vi)
ΔStotal=ΔS+ΔSsurrou­ndings
ΔG=nRT Σ xiln(xi) xi is mole fraction
ΔG = TΔStotal
 

Internal Energy (ΔU)

General
ΔU=q+w
Constant Volume
ΔU=CvΔT = qv
Adiabatic, Reversible
ΔU= w = n(Cpm-R)ΔT = nCvmΔT
Ideal
ΔU=nCvmΔT

Enthalpy (ΔH) (State Fxn)

General
ΔH= ΔU+Δ(PV) = ΔU+nRΔT
Constant Pressure
ΔH= CpΔT
Ideal
ΔH = qp
Constant Volume
ΔH= nCpmΔT + VΔP
Even More General
dH= (dH/dP)T dT + (dH/dT)P dP
Liquids & Solids
(dH/dP)T = V(1-Tβ)
Constant Pressure, closed system
ΔH= (Uf+PfVf)-(Ui+PiVi)
Isobaric
ΔH= n∫Cpm(T) dT = nCpmΔT

Exam 2 Material

Sm(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) `
For Ideal Gases: ΔSm=Rln(Vf/Vi)=-Rln(Pf/Pi)
ΔG(T2)/T2= ΔG(T1)/T1+ΔH(T1)(1/T2-1/T1)
Max Work: Revers­ible, adiabatic, isothermal
Hess's Law: Total Enthalpy change is indepe­ndent of # of steps(­pat­h-i­nde­pen­dent).
ΔA = ΔU-TΔS = ΔH-nRT (Hemholtz)
for ΔGor only include non-pure substa­nces.

Exam 3

ΔGR = ΔG°R+RT ln(QP)
ln(KP) = -ΔG°R/RT
Kx=KP(P/P°)-ΔV
dA = 𝛾 dσ gamma is surface tension
Work = 8pi𝛾r dr
Force = 8pi𝛾r
h(capi­llary rise/d­epr­ession) = 2𝛾/𝞺gr
𝓾B=𝓾°B+RTln(­𝛾[B]) gamma is activity coeffi­cient
ΔGR = ΔG°R-2.303­vRT(pH)
qx = kA(Tsi-Tso)/L
q''x= -k dT/dx = qx/A
Ėingout = Ėinternal
q12 = εσA(T14-T24) - Heat xchange via radiation b/t 2 surfaces
q''s = h(Ts-T) - Newton's Law of Cooling
       
 

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