Cheatography

# 313 Exam 3 Cheat Sheet by xsgirl99

### 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=m``s``/M``s`` ΔU``comb``+m``H2O``/M``H2O`` C``v,m``(H2O)Δ­T+ΔTC``calori­meter`` ΔHo=m``salt``/M``salt`` ΔHo``solution``+m``H2O``/M``H2O`` C``p,m``(H2O)Δ­T+ΔTC``calori­meter`` S=k ln(W) W=#of states Efficiency = 1-|q``cd``|/|q``ab``| <1 ΔHo``rt``=ΔHo``298``+∫ΔC``p``(T) dT from 298 to T ΔH``combustion`` = ΔU``combustion``+Δ(PV) For Solids & Liquids: ΔH~= ΔU Δs=-nRln(P``f``/P``i``)+∫nC``pm``/T dT for P``i`` to P``f`` Δs=nRln(V``f``/V``i``)+∫nC``vm``/T dT for V``i`` to V``f`` Isolated System: ΔS=q``p``(1/T``1`` - 1/T``2``) Isothe­rmal, Ideal: ΔS=nRln(V``f``/V``i``) ΔS``total``=ΔS+ΔS``surrou­ndings`` ΔG=nRT Σ x``i``ln(x``i``) x``i`` is mole fraction ΔG = TΔS``total``

### Internal Energy (ΔU)

 General ΔU=q+w Constant Volume ΔU=C``v``ΔT = q``v`` Adiabatic, Reversible ΔU= w = n(C``pm``-R)ΔT = nC``vm``ΔT Ideal ΔU=nC``vm``ΔT

### Enthalpy (ΔH) (State Fxn)

 General ΔH= ΔU+Δ(PV) = ΔU+nRΔT Constant Pressure ΔH= C``p``ΔT Ideal ΔH = q``p`` Constant Volume ΔH= nC``pm``ΔT + 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= (U``f``+P``f``V``f``)-(U``i``+P``i``V``i``) Isobaric ΔH= n∫C``pm``(T) dT = nC``pm``ΔT

### Exam 2 Material

 S``m``(T)=S``m``(0ok) +∫C``pm``/T dT(solid 0-T``f``) +ΔH``fus``/T``f`` + ∫C``pm``/T dT(liquid T``f``-T``b``) +ΔH``vap``/T``b`` ∫C``pm``/T dT(gas T``b``-T) ` For Ideal Gases: ΔS``m``=Rln(V``f``/V``i``)=-Rln(P``f``/P``i``) ΔG(T``2``)/T``2``= ΔG(T``1``)/T``1``+ΔH(T``1``)(1/T``2``-1/T``1``) 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 ΔGo``r`` only include non-pure substa­nces.

### Exam 3

 ΔG``R`` = ΔG°``R``+RT ln(Q``P``) ln(K``P``) = -ΔG°``R``/RT K``x``=K``P``(P/P°)-ΔV dA = 𝛾 dσ gamma is surface tension Work = 8pi𝛾r dr Force = 8pi𝛾r h(capi­llary rise/d­epr­ession) = 2𝛾/𝞺gr 𝓾``B``=𝓾°``B``+RTln(­𝛾[B]) gamma is activity coeffi­cient ΔG``R`` = ΔG°``R``-2.303­vRT(pH) q``x`` = kA(T``si``-T``so``)/L q''``x``= -k dT/dx = q``x``/A Ė``in``+Ė``g``-Ė``out`` = Ė``internal`` q``12`` = εσA(T``1``4-T``2``4) - Heat xchange via radiation b/t 2 surfaces q''``s`` = h(T``s``-T``∞``) - Newton's Law of Cooling