1. Thermodynamics and Statistical Mechanics
Class 11, 2/24/06
Thermodynamics and Statistical Mechanics
Review for Quiz 1

2. Laws of Thermodynamics
Class 11, 2/24/06
Laws of Thermodynamics
First law: đQ – đW = dU
Energy is conserved
Thermo & Stat Mech - Spring Class 11

3. Laws of Thermodynamics
Class 11, 2/24/06
Laws of Thermodynamics
Second Law: The entropy of an isolated system increases in any irreversible process and is unaltered in any reversible process. This is the principle of increasing entropy.
DS ³ 0
Thermo & Stat Mech - Spring Class 11

4. Laws of Thermodynamics
Class 11, 2/24/06
Laws of Thermodynamics
Third Law: The entropy of a true equilibrium state of a system at a temperature of absolute zero is zero.
Equivalent to: It is impossible to reduce the temperature of a system to absolute zero using a finite number of processes.
Thermo & Stat Mech - Spring Class 11

5. Class 11, 2/24/06
Second Law Variations
No series of processes is possible whose sole result is the absorption of heat from a thermal reservoir and the complete conversion of this energy to work.
There are no perfect engines!
Thermo & Stat Mech - Spring Class 11

6. Class 11, 2/24/06
Second Law Variations
No series of processes is possible whose sole result is the transfer of heat from a reservoir at a given temperature to a reservoir at a higher temperature.
There are no perfect refrigerators!
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7. Thermo & Stat Mech - Spring 2006 Class 11
Zeroth Law
If two systems are separately in thermal equilibrium with a third system, they are in thermal equilibrium with each other.
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8. Thermo & Stat Mech - Spring 2006 Class 11
Work done by a gas
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9. Thermo & Stat Mech - Spring 2006 Class 11
Ideal gas law
Ideal gas law: PV = nRT
In terms of molar volume, v = V/n,
this becomes:
Pv = RT, or P = RT/v
Thermo & Stat Mech - Spring Class 11

10. van der Waals equation of state
Class 11, 2/24/06
van der Waals equation of state
This equation has a critical value of T which suggests a phase change. The next slide shows graphs for several values of T .
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11. Thermo & Stat Mech - Spring 2006 Class 11
Thermal Expansion
Expansivity or Coefficient of Volume Expansion, b.
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12. Thermo & Stat Mech - Spring 2006 Class 11
Compressibility
Volume also depends on pressure.
Isothermal Compressibility:
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13. Thermo & Stat Mech - Spring 2006 Class 11
Cyclical Relation
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14. Thermo & Stat Mech - Spring 2006 Class 11
Carnot Cycle
A Carnot cycle is an idealized reversible cycle that operates between two heat reservoirs at temperatures T1 and T2, where T2 > T1. It can operate as a heat engine, or a refrigerator.
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15. Thermal Efficiency (h)
Class 11, 2/24/06
Thermal Efficiency (h)
If T1 = 0, h = 1 (100%)
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16. Thermo & Stat Mech - Spring 2006 Class 11
For a Carnot Engine or
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17. Thermo & Stat Mech - Spring 2006 Class 11
Entropy
For reversible processes.
Entropy is a state variable.
Thermo & Stat Mech - Spring Class 11

18. Thermo & Stat Mech - Spring 2006 Class 11
First and Second Laws
First Law: dU = đQ – đW
First law, combined with the second law:
dU = TdS – PdV
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19. Thermo & Stat Mech - Spring 2006 Class 11
Tds Equations
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20. Thermo & Stat Mech - Spring 2006 Class 11
Ideal Gas
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21. Thermo & Stat Mech - Spring 2006 Class 11
Properties
From first law: TdS = dU + PdV, or
Internal Energy dU = TdS – PdV U(S, V)
Enthalpy: H = U + PV
dH = TdS + VdP H(S, P)
Thermo & Stat Mech - Spring Class 11

22. Thermo & Stat Mech - Spring 2006 Class 11
New Potentials
Helmholtz Function:
F = U – TS
Gibbs Function:
G = U – TS + PV
G = H – TS
G = F + PV
Thermo & Stat Mech - Spring Class 11

23. Thermo & Stat Mech - Spring 2006 Class 11
All Four
dU = TdS – PdV U(S, V)
dH = TdS + VdP H(S, P)
dF = – PdV – SdT F(V, T)
dG = – SdT + VdP G(T, P)
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24. Thermo & Stat Mech - Spring 2006 Class 11
Maxwell Relations
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25. Clausius-Clapeyron Equation
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