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Thermodynamics Flashcards

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1
Q

Basic definition of enthalpy

(equation)

A

H = U + PV

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2
Q

Basic definintion of Gibbs free energy

(equation)

A

G = H - TS

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3
Q

Basic definition of Helmholtz free energy

(equation)

A

A = U - TS

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4
Q

Basic definitions of heat capacity

(equation)

A

Cp = [dH/dT]p = [dq/dT]p ; Cv = [dU/dT]v = [dq/dT]v

these are partial derivatives

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5
Q

Statistical definition of entropy

A

S = k lnW

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6
Q

Thermodynamic definition of entropy

(equation)

A

dS = dq(rev) / T

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7
Q

Basic definition of chemical potential

A

μ = Gm (molar gibbs energy) = [dG/dn(i)]p,T,n’

^partial derivative

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8
Q

1st law of thermodynamics

equation

A

dU = dq + dw

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9
Q

2nd law of thermodynamics

equation

A

dS >= dq/ T
and for a system at eqm: dS = dq/T

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10
Q

3rd law of thermodynamics

equation

A

S(0K) = 0
for a perfect crystal

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11
Q

master equation for U

A

dU = TdS - pdV

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12
Q

master equation for H

A

dH = TdS + VdP

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13
Q

master eqaution for A

A

dA = -pdV - SdT

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14
Q

master equation for G

A

dG = VdP - SdT

this is the first and 2nd laws in terms of P, V, S, and T

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15
Q

Isothermal change

A

processes where dt = 0
dU = dw

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16
Q

adiabatic change

A

a change where energy cannot be exchanged as heat between the system and surroundings - dq = 0
=> dU = dw

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17
Q

reversible change

A

sum of infinitesimal reversible steps where the system and surroundings are in equilibrium
=> all spontaneous processes are necessarily irreversible

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18
Q

What is Cp

A

(dH/dT)p = (dq/dT)p

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19
Q

What is Cv

A

Cv = (dU/dT)v = (dq/dT)v

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20
Q

How many degrees of freedom does a molecule made up of N atoms have

A

3N

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21
Q

What is equipartition theorem

A

Each quadratic degree of freedom contributes 1/2 RT to the internal energy, U

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22
Q

How can Maxwell’s equations be derived?

A

Maxwell’s equations are derived by relating the total differential of a thermodynamic quantity, i.e. U with their master equations and comparing coefficients

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23
Q

What is the 0th law of thermodynamics (in words)

A

if two systems are in thermodynamic equilibrium with a third system, the two original systems are in thermal equilibrium with each other

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24
Q

What is the 1st law of thermodynamics (in words)

A

energy can be converted from one form to another with the interaction of heat, work, and internal energy, but it cannot be created or destroyed

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25
what is the equation for work
w = - P(ex) ΔV (comes from dw = -p(ex)dV)
26
what is the equation for work done in relation to force?
w = - |F|z where z is the direction of the force
27
What is the definition of energy
Energy is the capacity of a system to do work in other words, if work is done onto a system, its capacity to do work increases such that its energy increases
28
what is a state function
a property with a value depending solely on the current state of the system - i.e. independent of the path taken
29
does reversible or irreversible expansion of a gas require more work done
reversible - this is illustrated by a p-V diagram where for a reversible process pV^γ is constant whereas for an irreversible process p is constant (horizontal line) and the work done is the area under the curve.
30
work done during free expansion
zero
31
what is a path function
physical quantities whose values depend on the path between two states e.g. work and heat
32
what are the two types of irreversible processes
1. impossible processes = cannot occur under a given set of conditions 2. possible/spontaneous processes = can occur but not reversibly
33
what is Duhem's theorem
for a closed system which undergoes a reversible change in which only p-V work is done, specifying how some pair of state functions changes is sufficient to specify how the state of the system changes.
34
when does duhem's theorem not apply
a particular pair of state functions may not be sufficient if there are changes in the number of phases present ## Footnote e.g. water-water vapour equilibrium
35
what is the integrated equation for work done during isothermal reversible expansion
w = - n R T ln (Vf / Vi)
35
what can be said about the work done during a reversible process
maximum work of any kind is done when a process occurs reversibly
36
what is the heat transfer at constant pressure
Δ H = q where q is the heat transferred at constant pressure
37
How do you derive the relationship between enthalpy chabge and heat transfer at constant pressure
1. derive dH = dq + Vdp 2. at constant pressure dp = 0
38
Relate Cp and Cv
Cp - Cv = nR
39
temperature dependence of ΔrH (Kirchoff's Law)
ΔrH(T2) = ΔrH(T1) + ∫ ΔrCp dT where ΔrCp is the difference in the stoichiometrically weighted heat capacities of the products and reactants
40
What is the 2nd law of thermodynamics (in words)
the state of entropy of the entire universe, as an isolated system, will always increase over time. changes in the entropy of the universe can never be negative
41
how can the entropy change of the surroundings be quantified when no work is done
if no work is done then for the surroundings: dq(sur) = dU(sur) so dS(sur) = dU(sur)/T
42
what is the entropy change for an adiabatic process
zero
43
what is the Clausius Inequality
dS >= dq/T
44
Describe how to derive the Clausius Inequality
1. dw(rev) > dw 2. dU = dq + dw = dq(rev) + dw(rev) 3. dq(rev) >= dq 4. dS = dq(rev)/T
45
What are the consequences of the Clausius Inequality
* entropy cannot decrease in a spontaneous change * spontaneous processes are necessarily irreversible | Clausius Inequality: dS >= dq/T
46
what is Δ(trs)S at T(trs) where trs indicates equilibrium at a phase transition
Δ(trs)S = Δ(trs)H/T(trs)
47
What is Trouton's Rule
a wide range of liquids give approximately the same Δ(vap)S
48
what are deviations from Trouton's Rule a result of
deviations are as a result of strong intermolecular interactions resulting in partial ordering of the molecules in the liquid
49
temperature dependence of entropy
ΔrS(T2) = ΔrS(T1) + ∫ ΔrCp/T dT where ΔrCp is the difference in the stoichiometrically weighted heat capacities of the products and reactants
50
how can you derive an equation of sate in the form p = p(V,T)
1. write dS for S(V,T) 2. sub into dU = TdS - pdV 3. compare with dU for U(V,T) 4. rearrange to get: p = T (dp/dT)v - (dU/dV)T
51
what is the Gibbs-Helmholtz equation
(d(G/T)/dT)p = -H/T^2
52
Describe how to derive the Gibbs-Helmholtz equation | describes temperature dependence of gibbs
1. Obtain Maxwells equations: (dG/dT)p = -S 2. G = H - TS so (dG/dT)p - G/T = -H/T 3. substitue into: (d(G/T)/dT)p = 1/T (dG/dT)p - G/T^2 ## Footnote note that step 3 is just implicit differentiation of G/T
53
Derive pressure dependence of Gibbs free energy
1. Obtain Maxwell's equation (dG/dp)T = V 2. integrate wrt p to give: G(p2,T) = G(p1,T) + ∫ V(p,T)dp
54
what is the constraint for phase equilibria
molar Gibbs energy of all phases must be equal
55
What is the phase rule for a single-component system
F = 3 - P F is the number of degrees of freedom (i.e. directions in the p,T plane which are accessible without violating equilibrium) P is the number of phases in equilibrium
56
What is the Clapeyron equation
dp/dT = ΔS/ΔV or dp/dT = ΔH/(T ΔV) both are equivalent
57
Describe how to derive the Clapeyron equation for the slope of the phase boundary
1. write down the master equations for dG of the two phases (a,b) in equilibrium 2. since G(a) = G(b) then dG(a) = dG(b) if they are in equilibrium after the change 3. equate and rearrange to give the Clapeyron equation 4. second form is obtained by using ΔG = ΔH - TΔS and the fact ΔG = 0 at eqm
58
What are the assumptions which are used to convert the Clapeyron equation into the Clausius-Clapeyron equation
ΔV ~ V(gas) ideal gas so V(gas) ~ RT/p so 1/p dp/dT = dlnp/dT = ΔH/(R T^2)
59
Generalise dG to the multi-component case
dG = Vdp - SdT + Σμdn
60
relate dn and dξ
dn = v dξ where dn is change in moles v is stoichiometric coefficient ξ is the extent of reaction (reactants at ξ = 0 and products at ξ = 1)
61
if dn = v dξ, what is the equation for μ in terms of μ(standard) for an ideal gas
μ = μ(standard) + RTln(p/p(standard)) otherwise, μ = μ(standard) + RTln(a)
62
derive the relationship between ΔrG and K
1. combine ΔrG = Σvμ and μ = μ(standard) + RTln(p/p(standard)) 2. simplify to obtain ΔrG = ΔrG(standard) + RTlnQ 3. at equilibrium ΔrG = 0 so.... ΔrG(standard) = -RTlnK | Q is the reaction quotient, Q = K at equilibrium
63
What is the van't Hoff equation for the temperature dependence of the eqm constant K
(dlnK/dT)p = ΔrH(standard)/(R T^2)
64
Describe how to derive the van't Hoff equation for the temperature dependence of the equilibrium constant
1. derive ΔrG(standard) = -RTlnK 2. derive the Gibbs-Helmholtz equation for the temperature dependence of the Gibbs free energy (d(ΔrG(standard)/T)/dT)p = -ΔrH(standard)/T^2 3. Combine the two to get (dlnK/dT)p = ΔrH(standard)/(R T^2)

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