Introduction to thermodynamics

Topics First law of thermodynamics. Deﬁnitions of internal energy and work done, leading to dU = dq + dw. Heat capacities, Cp = CV + R. Reversible and irreversible processes. Various types of expansion, isothermal, adiabatic. CV and Cp according to kinetic theory, monatomic gases, other gases. The meaning of temperature, empirical temperature scale, perfect gas scale, the second law of thermodynamics, thermodynamic temperature scale. So far, we have concentrated upon developing a microscopic model for the behaviour of gases. We now turn our attention to the macroscopic description of solids, liquids and gases, which is concerned with the bulk properties of properties of substances. This is the subject of thermodynamics and, in contrast to our analysis so far, we deny that the various forms of matter are actually composed of atoms and molecules. Thermodynamics is a large and very powerful branch of physics. In this chapter, we show how thermodynamics can provide crucial clues about the physics of our microscopic model.

6.1 First Law of Thermodynamics

The ﬁrst law of thermodynamics is a statement about the conservation of energy.

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Statistical and Quantum Physics Energy is conserved when heat is taken into account.

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This is a somewhat more subtle statement than might appear at ﬁrst sight. We have deﬁned the heat capacity in terms of the amount of heat needed to raise the temperature of a substance by one degree, but we have not stated what heat is. The most rigorous approach is to deﬁne ﬁrst of all the internal energy U of the system. We have already introduced this concept in our discussion of the internal energy of an ideal gas, but we can now generalise it to any substance or system. A material can store energy in many diﬀerent ways besides molecular motions - the molecules may vibrate and rotate, the material may be placed in an electric or magnetic ﬁeld, the energy density of radiation may be important and so on. Therefore, we need a general way of coping with all these possibilities. In general, there are two ways in which the system can acquire internal energy • We can do work on the system and so increase its internal energy. • We can allow heat Q to enter the system. The ﬁrst statement is fundamental since it asserts that, by doing work on the system alone, we can raise the internal energy to any given value, quite independent of what we might mean by heat. This is the clue to how we deﬁne what heat is. We write down the expression for the change in internal energy due to both causes. dU = dQ + dW, (6.1)

The ﬁrst law of thermodynamics dU = dQ + dW

where dW is the work done on the system. This expression is a formal statement of the ﬁrst law of thermodynamics. Note how we interpret this statement. The internal energy U is a well-deﬁned physical quantity which we can measure. The amount of work done dW can

Statistical and Quantum Physics

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be measured also. We deﬁne the heat entering the system dQ to be the quantity dQ = dU − dW. (6.2) Figure 6.1. The cylinder and piston. . . .......................................................................... . ............................................................................ . . . . . . . . . . . . .. .... ....................................................................... . . .................................................................... . . . . . . .. . . . ....... . . . . . . . . . .. . . . . . . ....... . . . . . . . . . . . ....... . . . . . . . . .... . . . ....... . . . . . . . . . . .. . . . . . . ....... . . . . . . . . . . . ....... . . . . . . . . . . .... . . . ....... . .......................... ......................... .. . . . . . . . . . .. . . . . . ................................. .. . . . . . . ............ . . . . . . . . . . ....... .......................... . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . ....... .......................... ....