lecture+2+thermodynamics ma (1)

8/3/2019 Lecture+2+Thermodynamics MA (1)

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Pressure-temperature-volume properties (equations of state); water, UO2

Vapor pressures: fuel, coolant, fission products

Thermal properties: the specific heat; coefficient of thermal expansion

Phase diagrams; single component, binary and higher order

Chemical and physical state of fission products in fuel

Tendency of hydrogen to form hydrides in cladding and carbon to form carbides in steel

Susceptibility of metals and alloys to aqueous corrosion

Response of uranium dioxide stoichiometry to the oxygen potential of the environment

Point-defect populations in solids

Where are thermodynamics relevant in a LWR?


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Review of Basic Thermodynamics

1. Basic Thermodynamic Properties

2. First Law of Thermodynamics

3. Second Law of Thermodynamics

4. (Third Law of Thermodynamics)5. Single Component Phase Equilibria

6. The Gibbs Phase Rule

7. Solution Thermodynamics

8. Binary Phase Diagrams and the Lever Rule

9. Ternary Phase Diagrams


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Five fundamental thermodynamic properties:

Three derived thermodynamic properties:

1. Basic Thermodynamic properties

* Intensive properties -- independent of the system size

*

*

e.g., v=V/n specific volume an intensive property

Also: H= H/n, g= G/n (n = # of moles)


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The heat capacities (also called specific heats):

The coefficient of thermal expansiona and

the coefficient of compressibilityb:


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2. First Law of Thermodynamics

The First law of thermodynamics is an empirical observation, neverrefuted, that the change in the internal energy of a closed system

resulting from addition of heat and performance of work is given by:

U = Q - W (eq. 1.7)

whereU = U(final) - U(initial) = change in system internal energyQ = heat added tothe systemW = work done bythe system (e.g., mechanical, chemical, electrical)

U + Usurr = 0


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3. Second Law of Thermodynamics

S+Ssurr 0

In an isolated system, for any spontaneous processthe entropy will either increase or remain the same.

du = Tds - pdv

Combining the 1st and 2nd laws of thermodynamics:

dh = Tds + vdp

dg = -sdT + vdp

df = -sdT - pdv

Where equality applies to reversible processes, i.e., at equilibrium

S

Q

T


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Arrive at the following relations at fixed temperature:

dG = -SdT + Vdp = dH TdS SdT = dH TdS

dF = -SdT pdV = dU TdS SdT = dU TdS

Note that dH = dU pdV V dp = dUd(pV)

For solid phases, dU ~ dH, use H and U interchangeably.

From S+Ssurr 0 in an isolated system,

can derive dG 0 (~dF 0) in an isothermalsystem.

The criterion for equilibrium: F / G is minimized


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Free Energy vs. T across Tm for a Solid and a Liquid

Whether a substance will be solid, liquid or gaseous, depends on whichphase has the lowest Gibbs free energy. When two phases coexist, theirspecific Gibbs free energies are equal.

Gliq

Gsolid

G

temperature

Tm


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(eq. 1.19a)

(eq. 1.19b)

Saturation pressure (or vaporpoint)

The pressure at a corresponding Tat which liquid boils into its vaporphase or a solid sublimate into itsvapor phase

Important application:


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Phase Diagram of a Pure Substance

(eq. 1.22)

(eq. 1.19a)

(eq. 1.19b)


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7. Solution Thermodynamics

Mole Fraction of a component:

For an ideal solution*

(A and B are the constituent elements,xA and xB, their concentrationsq is the intensive quantity of any property)

*A binary solution of A

and B is ideal if theaverage of the A-A andB-B intermolecularforces is just equal to thestrength of the A-Binteraction.

Solution: a homogeneous solid or liquid system of two or more components

The chemical potential:

When q=entropy, an additional term appears on the r.h.s.:


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Raoults law (for an ideal solution): Henrys Law (for a nonideal solution):

The Henrys law constant, kHA, is the product of the composition-independent activitycoefficient of A in solution and the saturation pressure of pure A. In the concentration rangewhere A follows Henrys law, component B must obey Raoults law.


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8. Binary Phase Diagrams and the Lever Rule

(note: contrary to the implication in the text, this is not the correct U-Zr phase diagram)

The lever rule:

alloy composition

solid composition liquid composition


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The phase diagram is determined by the phases free energies


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The Eutectic Phase Diagram

Eutectic Point


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Lever rule applied to a binary system

A BC

C = 65 weight% B

Point 1 Liquid only

Point 2b starts to form. Phase b first forms with acomposition of 96 weight% B. The green dashed linebelow is an example of a tie-line. A tie-line is ahorizontal (i.e., constant-temperature) line throughthe chosen point, which intersects the phaseboundary lines on either side.


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A BC

C = 65 weight% B

Point 3

C1 58 weight% BC2 92 weight% Bfraction of solid b (65 - 58) / (92 - 58) 20 weight%fraction of liquid (92 - 65) / (92 - 58) 80 weight%


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A BC

C = 65 weight% B

Point 4

C3 48 weight% BC4 87 weight% Bfraction of solid b (65 - 48) / (87 - 48) 44 weight%.As the alloy is cooled, more solid b phase forms.The remainder of the liquid becomes a eutectic phase of a+bfraction of eutectic 56 weight%


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Point 5

C5 9 weight% BC6 91 weight% Bfraction of solid b (65 - 9) / (91 - 9) 68weight%fraction of solid a (91 - 65) / (91 - 9) 32weight%


A BC

C = 65 weight% B


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The Iron-Carbon Phase Diagram

Wt% C
http://www.sv.vt.edu/classes/MSE2094_NoteBook/96ClassProj/examples/no_clim.html


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9. The Ternary Phase Diagram

In ternary systems (involving 3 components), Gibbs phase rule predicts a maximum of:

F = C - P + 2 = 3 - 1 + 2 = 4

degrees of freedom when only a single phase is present. In depicting these diagrams

usually both pressure and temperature are held constant and the composition variables

plotted against each other on a triangular diagram:

A

B C25 50 75

25

50

75

75

50

25

weight or mole percent C

Locate the point on the above ternary phase diagram where the system

consists of 25% A and 50% B.


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A

B C25 50 75

25

50

75

75

50

25

weight or mole percent C

cB = 25%

cA = 25%

cC = 50%


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Example of a ternary phase diagram

of NaCl, KCl, H2Oat a fixed pressure of 1 atm

1413oC

H2O NaCl

KCl

0oC

1500o

C

liquid

solution

solid

solution

isothermal slice at

25oC


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Ternary phase diagram for Fe, Cr, Ni at 400Cshowing commercial alloys related to PWR steam generators

lecture+2+thermodynamics ma (1)

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