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