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Heat (>, <, or = 0?)
- If q>0, then heat is added to the system
- If q<0, then heat is removed from the system
- If q=0, then dU=w
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Work (> or < 0?)
- If w>0, work is being done on the system.
- If w<0, work is being done by the system.
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Internal Energy (dU) --> Any Conditions
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Heat --> General (Any Conditions)
q = c(dT)
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Enthalpy Change --> Any Conditions
- dH = dU + d(PV)
- dH = ncp(dT)
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Work Against a Constant External Pressure
w = -Pext(dV)
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Reversible, Isothermal Work
w = -nRTln(V2/V1)
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Work at Constant Volume
w = 0
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Relate cp and cv
cp = cv + R
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Heat at Constant Volume
- q = ncv(dT)
- Note: This also equals dU, because at constant volume, w=0.
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Heat at Constant Pressure
- q = ncp(dT)
- Note: This also equals dH
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Enthalpy
- A state function that represents the heat transferred for a system under constant pressure (qp)
- dH = dU + d(PV)
- For an ideal monatomic gas, this can be rewritten as: dH = dU + d(nRT)
- dH = qp = ncp(dT)
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Molar Heat Capacities for Ideal, Monatomic Gases at Constant V and Constant P
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Boltzman's Equation
- S = KBln(omega)
- KB = 1.38 x 10-23 J/K
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Entropy Change for Reversible, Isothermal Expansion
- dS = nRln(V2/V1)
- dS = qrev/T
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Entropy Change at Constant Pressure
dS = ncpln(T2/T1)
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Entropy Change at Constant Volume
dS = ncvln(T2/T1)
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Entropy Change for Phase Changes
dS = (dHPT)/T
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dSuniverse and Spontaneity
- If dSuniv > 0, the process is spontaneous as written
- If dSuniv < 0, the process is spontaneous in the reverse direction
- If dSuniv = 0, the process is at equilibrium
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Gibbs Free Energy
dG = dH - TdS
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