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System. The idea of a system is very important in thermal physics. In general terms, the word "system" means an aggregation or collection of things which are interdependent on each other. What is significant in thermal physics is that although material systems may be very complex in their internal structure (of molecules etc.), they can be treated as a whole. A gas in a cylinder, a liquid in a flask, or a metallic crystal, are all examples of systems: in each case, there is a definite fixed mass of substance; there is some form of containment (the cylinder, the flask, the crystal lattice) or enclosure ; and the material can be treated as effectively the same throughout.

The criterion of "sameness" to which we just referred is also very important for the whole of thermal physics. Being "effectively the same throughout", e.g. no internal variations of density, or temperature, is a rough way of saying "being in equilibrium".

State of a system. A system in equilibrium is said to be in a particular state. This state is specified by certain key parameters, or measurable properties, such as pressure, volume, temperature, etc. It is usually not necessary to specify more than three such parameters in order to have a complete specification (that is to say, if we had parameters a, b, c and d, and we specified a, b and c, then d could have only one value fixed by the values of a, b and c).

Now, these parameters of state enable us to represent the behaviour of systems in mathematical formulae and on graphs. The complex internal life of a system is reduced to a series of points on a graph, or to an expression relating two parameters. For instance, the possible states ol' a mass of "ideal" gas at constant temperature can be represented as a line in the following way:

Alternatively, they can be represented as a formula:
P.V = constant
The graph in the illustration above uses axes of pressure and volume. Pressure as "force per unit area" is a mechanical parameter-that is, we can understand it in terms of mechanics alone. So the pressure-volume region is a mechanical plane of representation. There are many such planes; another example is that of the H (magnetic field)-I (magnetization) region, important for paramagnetics. Thermal parameters such as temperature do not belong to any mechanical plane. Part of our study here concerns how the thermal is related to the mechanical. What are known as the Laws of Thermodynamics serve just that purpose, and in this Study Unit we shall come across the First Law of Thermodynamics.

Work. Mechanics gives us the rules for measuring the quantity of energy transferred by work. The more elementary formulation is to say that:
Work = Force x Displacement
However, there is a better way, and one far more suited to thermal physics. Some preliminary explanation is needed. When we deal with work in the gravitational field we have to find out what are the gravitational forces; when we deal with work in electricity, we have to find out what are the electrical forces, and so on. The resulting expression may then contain nothing explicitly to do with forces or displacements as such. For example, in the case of magnetization:
Work = HdI

where H is the magnetic field and dI is an infinitesimal increase in magnetization. In the case of a gas expanding, the work it does is:
Work = PdV

where P is the pressure and dV is an infinitesimal increase in volume. The pattern is always the same: we have the product of one parameter which represents the intensity at which the work is done, e.g. pressure, field strength, force, etc., and the corresponding increase in another parameter, e.g. volume, magnetization, distance, etc. Parameters of the first kind are called intensive parameters (we can represent them as Y) whereas parameters of the second kind are called extensive parameters (we can represent them as X). So we can write down a general expression for work:
Work = YdX

where Y is the intensive parameter and X the corresponding extensive one. We will generalize the scheme in Study Unit 3 to encompass thermal energy transfer. In the above expression, both Y and X must be parameters of the system (in equilibrium). Then changes in these parameters can be interpreted also as changes in the energy of the system.

Internal energy. We are going to combine together two fundamental ideas: system and energy transfer.
Though a system may not be moving and may appear utterly inert, this is because of its condition of equilibrium. it has, nevertheless, a certain internal energy. This is given the symbol U. For our purposes, right away we can say such things as, "the hotter a system is, the greater its internal energy", and "if work is done on a system then its internal energy increases". (Digression. In this discussion, we are not going to delve into the problems of how the thermal parameters of temperature and entropy are derived; these are reserved for Study Units 4 and 3 respectively. So when we use the term "hotness" we are talking about temperature in a deliberately rough and ready way to mean thermal intensity as measured by any familiar thermometer.)

If we can put energy into a system and we can take energy from a system, then it clearly does make sense to think of the system as "having" a certain energy of its own. The problem is to relate together the energy changes we can observe in terms of temperature and those we can measure in terms of work.

The work of Joule. We can now pin down some of this discussion to actual experimental work. Joule, in his classic experiments, wanted to demonstrate convincingly that for a given quantity of energy put into a system the result was the same, no matter what form the source of' energy had. His system consisted of water in a calorimeter. His sources of energy were a raised weight (that iii falling turned paddle wheels that churned the water), an electrical battery (heating the water through all electrical element), and chemical reactions. In each case, he calculated the work expenditure and he supposed that this energy entered the system. The same input of energy was found to produce the same rise in temperature for the same mass of water under the same conditions.

Adiabatic changes. Joule, in putting energy into his system, had used some kind of "friction". He did not do work on the system (be clear about this).

When work is done on a system, its state as represented on the mechanical plane must alter. For example, in compressing a gas the work done is:
W = - PdV
For a finite change, as from A to B on the graph shown in fig. 2.2:

Changes which are produced by work alone, on or by the system, are called adiabatic changes. By the principle of the conservation of energy, we have in the case of a gas:

Let us make a generalized picture of adiabatic changes for a system. Such changes can be represented as lines on some mechanical plane, and one of the axes will be intensive (such as pressure) and the other extensive (such as volume)-see fig. 2.3.

If the state of the system belongs to line A, say, then adiabatic changes will not shift it from that line. So if the state of the system jumps from line A to line B, or to line C, then something other than work is bringing this about. This something other is called heat.

The First Law of Thermodynamics. The First Law is concerned with changes or transfers of energy. The first basic idea incorporated into it is:

The second basic idea is that there are two distinct means of energy transfer: work (W) and heat (Q). The two ideas are combined in one symbolic statement:

Q = U + W

Q represents total quantity of energy transferred by heat to system.
W represents total quantity of energy transferred by work away from system.
U represents total increase of internal energy of system.

Complexity of the internal energy. The First Law appears simple but requires care in its application. It represents the conservation of quantities of energy - however they are transferred and whatever form they take. We need to take some particular cases to illustrate the meaning of the symbolic expression.

(i) Change of state: A gas is "heated up"; it is then allowed to expand. At first, it gains energy by heat transfer; then it loses energy by doing work. The two quantities of energy can be made the same. The energy gained and then lost by the system means an increase followed by a decrease of its internal energy. The gas does not return to the same state, even though it returns to the same internal energy. At the end of the expansion, the volume is greater than at the beginning. Thus, the same internal energy of a system can correspond to a whole range of states, i.e. values of P, V and T.

(ii) Chemical energy: Whenever a change is made in the internal structure of a system, there is a change in the chemical energy. Examples of such changes are: going into solution, change of phase, ionization, and chemical combination.

The change in chemical energy is measured as a transfer of energy by heat. It is given the special symbol H (H is not a general symbol for heat) and called the heat of reaction, with units k cal mole . H is measured at constant temperature (usually 25°C) and at constant volume. When it is negative, it signifies a heat transfer out of the system and a loss of energy by the system. From the First Law:
H = U + W

At constant volume W = 0, so that H = U. For an exothermic reaction H < 0, and for an endothermic reaction H > 0.
A well known example of a "heat of reaction" is latent heat. Here there is a change of internal structure, in going from say, the liquid phase to the vapour phase of a substance. Such a change alters the amount of internal energy "locked-up" in a potential form in the molecules and in their interactions.

(iii) Expansion into a vacuum: When a gas expands into a vacuum it does no work and the whole process is so quick that no heat transfer takes place. An actual gas will cool. From the First Law:
U = Q - W; and thus H = 0
That is, the gas cools without a decrease of its energy. Therefore the temperature is not the only measure of the internal energy. In this instance, volume proves to be significant also. With two variables, the result of a change in one of them can be offset by a change in the other.

Two kinds of energy store. A store of energy is a reservoir from which energy can be taken and to which energy can be added. There are two kinds of energy store, which differ in the way that they store energy: internal enerqy (U) and potential energy(E). The transfer of energy from one store to another is by heat or by work:

E -> E work transfer, U -> U heat transfer,
E -> U work transfer, U -> E work transfer.

Some problematical situations:
(i) Electrical heating. We must have two stages of transfer together. This is a "transition" of energy or a work/heat transfer of energy.

(ii) Chemical reaction. We divide the internal energy into two parts, by analogy with the division of energy states into two kinds.

We can then interpret an exothermic reaction as a work transfer. By analogy with electrical heating, we can suppose that there is some intermediary internal energy U". Then:
U" would be the internal energy corresponding to intermediate states of the reactants when they are neither separate nor combined. These intermediate states are an important study in modern chemistry.

(iii) Joule expansion. A gas expands into a vacuum and cools. We divide the internal energy into two parts:

where E" represents the potential energy due to intermolecular forces. The transfer of energy from the thermal state to the potential state-a work transfer-means that the gas cools.

In general, we can say that thermal energy is that part of the internal energy which varies with temperature.