Free energy Flashcards
what’s the availability of a system
ΔA = Δ(E-T₀S+P₀V)
ΔA≤0 for a spontaneous change of constant temp and press
where does the Helmholtz free energy come from
dE = TdS - PdV
dE= TdS + SdT - SdT - PdV
dE= d(TS) - SdT - PdV
d(E-TS)= -SdT - PdV
F= E - TS
dF= dE - TdS (expand F at constant vol + temp)
where does the Gibb’s free energy come from
d(E-TS) = -SdT - PdV
d(E-TS) = -SdT +VdP - VdP - PdV
d(E-TS) = -SdT + VdP - d(PV)
d(E-TS+PV)= VdP - SdT
G= E - TS + PV
dG= dE - TdS + PdV (expand G at constant temp + press)
where does the enthalpy equation come from
d(E-TS+PV)= VdP - SdT
d(E-TS+PV) = VdP +TdS - TdS - SdT
d(E-TS+PV) = VdP +TdS - d(TS)
d(E+PV) = VdP + TdS
H= E + PV
dH= dE + VdP (expand H at constant entropy + press)
how to get the coefficients in the free energy equations in terms of a partial derivative
take Gibbs energy for example:
dG= VdP - SdT
if Temp is constant then dT=0 so -SdT=0
dG= VdP
V=dG/dP
∴ V= (∂G/∂P)ₜ (subscript t means temp is constant)
whats the availability for a thermally isolated system
thermally isolated: Q=0
ΔA = ΔE + P₀ΔV = 0
∴ ΔE = -P₀ΔV (just as for adiabatic processes)
so the change in internal energy is minimised
what’s the maxwell equation derivation method
take internal energy as an example
dE = TdS - PdV
dE =(∂E/∂S)ᵥ dT + (∂E/∂V)ₛ dV
∴ T= (∂E/∂S)ᵥ and P= - (∂E/∂V)ₛ
differentiate both sides of each equation partially with respect to the variable that’s held constant. hold the opposite variable constant
(∂T/∂V)ₛ = ∂/∂V * (∂E/∂S)ᵥ and (∂P/∂S)ᵥ = ∂/∂S * (∂E/∂V)ₛ
since ∂/∂V * (∂E/∂S)ᵥ = ∂/∂S * (∂E/∂V)ₛ :
(∂T/∂V)ₛ = (∂P/∂S)ᵥ
(exact same process but applied to F, G and H)
what does the Gibb’s free energy tell us
the direction of spontaneous process (for a reversible reaction) and constant temp and press
what does the Helmholtz free energy tell us
its decreasing for a spontaneous process at constant temp and vol
whats the triple point and critical point
Points on a pressure (y) - temperature (x) graph
triple point: temp and press at which all 3 states of matter can exist for a single substance
critical point: temp at which the liquid and gas form for a single substance is indistinguishable (superfluid)
derive the equation of state for a real gas
PV = nRT (ideal gas)
P –> P + a*(n/V)² (a: a constant unique to each type of gas)
V –> V - nb
[P + a(n/V)²][V - nb] = nRT
P + a(n/V)² = nRT/(V - nb)
P= nRT/(V - nb)- a*(n/V)²
this is also called the Van der Waals equation
what’s the Clausius - Clapeyron equation
the equation describing points of phase coexistence on a P - T graph
dP/dT = ΔSᵐ/ΔVᵐ = ΔHᵐ/ (T * ΔVᵐ)
the superscript m isn’t a power. it means ‘per mole’
how do you find the critical temperature
use the real gas equation
P= nRT/(V - nb)- a*(n/V)²
when the temp is the critical temp:
(∂P/∂V)ₜ = (∂²P/∂V²)ₜ = 0
