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CHAPTER 12
FREE ENERGY
12.1 Review of Internal Energy and Enthalpy
We are by now familiar with the equations
dU = TdS PdV and dH = TdS + VdP,
and with the ideas that the increase in the internal energy is the heat added at constant
volume and the increa
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CHAPTER 2
PARTIAL DERIVATIVES
2.1 Introduction
Any text on thermodynamics is sure to be liberally sprinkled with partial derivatives on
almost every page, so it may be helpful here to give a brief summary of some of the more
useful formulas involving pa
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CHAPTER 8
HEAT CAPACITY, AND THE EXPANSION OF GASES
8.1 Heat Capacity
Definition: The heat capacity of a body is the quantity of heat required to raise its temperature by
one degree. Its SI unit is J K1.
Definition: The specific heat capacity of a subst
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CHAPTER 13
EXPANSION, COMPRESSION AND THE TdS EQUATIONS
13.1 Coefficient of Expansion
Notation: In an ideal world, Id use , , respectively for the coefficients of linear,
area and volume expansion. Unfortunately we need for the ratio of heat capacities.
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CHAPTER 10
THE JOULE AND JOULE-THOMSON EXPERIMENTS
10.1 Introduction
Equation 8.4.3, TV 1 = constant , tells us how to calculate the drop in temperature if a gas
expands adiabatically and reversibly; it is expanding against an external pressure (e.g., a
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CHAPTER 5
THERMODYNAMIC PROCESSES
We shall be considering what happens when we perform certain processes on various systems. The
processes will usually entail either doing work on a system or adding heat to it, or perhaps we shall
allow the system to do
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CHAPTER 15
ADIABATIC DEMAGNETIZATION
15.1
Introduction
One way to cool a gas is as follows. First compress it isothermally. This means compress
it in a vessel that isnt insulated, and wait for the gas to lose any heat that is generated so
that it return
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CHAPTER 14
THE CLAUSIUS-CLAPEYRON EQUATION
Before starting this chapter, it would probably be a good idea to re-read Sections 9.2 and
9.3 of Chapter 9.
The Clausius-Clapeyron equation relates the latent heat (heat of transformation) of
vaporization or c
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CHAPTER 9
ENTHALPY
9.1 Enthalpy
Enthalpy is sometimes known as "heat content", but "enthalpy" is an interesting and unusual word,
so most people like to use it. Etymologically, the word "entropy" is derived from the Greek,
meaning "turning" (I'm not sur
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CHAPTER 16
NERNSTS HEAT THEOREM AND THE THIRD LAW OF
THERMODYNAMICS
16.1 Nernsts Heat Theorem
At the beginning of the twentieth century, Walther Nernst (Nobel Prize in Chemistry
1920) had investigated heat capacities and heats of reaction at progressive
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Carter 2-3.
(a) The gas satisfies the ideal gas equation equation PV = NRT, which can also be
written Pv = RT/ , where v is the specific volume or volume per unit mass and is the
molecular weight. Eliminate v from this and P = Av to obtain
P2 .
RT
A
(b
19
But we have already shown that AV 2
RT , and so the work done on the gas is
1
2
But T2
1
T,
4 1
R(T1
T2 ).
and therefore the work done on the gas is
3
8
RT1 .
=
Carter 3-4. Volume of 10 kg of ice =
10
m3.
916.23
Volume of 10 kg of water =
10
m3.
999.84
28
Carter 4-5. Note: The atomic weight (mass) of Cu is 63.5 amu, not 29 as given,
Specific heat capacity =
2.6 10 4
63.5
409.449 J kg 1 K 1.
Heat (energy) required to raise mass m through 100 K = 40944.9 m J.
Rest mass energy = mc2.
Fractional increase in
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CHAPTER 3
TEMPERATURE
3.1 Introduction
During our studies of heat and thermodynamics, we shall come across a number of simple, easy-tounderstand terms such as entropy, enthalpy, Gibbs free energy, chemical potential and fugacity,
and we expect to have n
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CHAPTER 11
HEAT ENGINES
11.1 Introduction
In my rarefied, theoretical, academic and unpractical mind, a heat engine consists of a
working substance obeying some idealized equation of state such as that for an ideal gas,
held inside a cylinder by a pisto
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hit the bag with an upwards-directed impulsive force, but this force does not move
through a distance, and so no further work is done on or by the bag. Thus the net work
done on the bag during the fall and the impact is mgh. However, this energy mgh is
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CHAPTER 7
THE FIRST AND SECOND LAWS OF THERMODYNAMICS
7.1 The First Law of Thermodynamics, and Internal Energy
The First Law of thermodynamics is:
The increase of the internal energy of a system is equal to the sum of the heat added to the system
plus t
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CHAPTER 4
THERMAL CONDUCTION
4.0 The Error Function
Before we start this chapter, lets just make sure that we are familiar with the error function erf a.
We may need it during this chapter.
Here is a graph of the gaussian function y =
1
ex .
2
4.0.1
0.7