# Basic thermodynamics

Part of the School of Physics

This class provides a basic overview requiring very little prior mathematical knowledge besides basic algebra. For a more involved discussion of thermodynamics which includes detailed derivations of these laws from first principles, please see the class page Statistical mechanics.

Thermodynamics is the study of temperature, chemical energy, and the properties of matter as a consequence of its atomic structure. In the discipline of thermodynamics, two areas of interest are most significant: macroscopic thermodynamics, which deals with the properties of bulk matter; that is, large quantities of matter on a 'human' scale of understanding, and statistical mechanics, which relates the macroscopic behavior of matter to microscopic behavior.

## Heat and Temperature

First of all, we must make clear some important definitions which may be different to the kind of language you are used to. In normal conversation, the words heat and temperature are used interchangably. To 'warm' or 'heat' something up is to increase its temperature. One might say 'that fire has a lot of heat in it'.

In physics however, the word heat has a very distinct meaning. Heat is a form of energy which is held in matter by the constant jostling of its particles. In macroscopic thermodynamics, heat can be thought of as a massless, invisible substance that can flow from one region to another, but it is very important to remember that this is NOT a real or accurate description of heat, merely a tool to help you visualise how matter and the energy contained within it behaves in the 'real world' as we see it. In reality, heat is an effect of the movement of particles - whether they be atoms, ions, molecules, electrons, photons or any kind of fictional 'magic' particle you could care to imagine. Particles transfer heat between one another by colliding with one another, and over time this will cause heat to flow around in large bodies of matter where it allowed to.

Heat is represented in a formula by the symbol Q, and its units, like other forms of energy, are Joules, which have the symbol J

Example: The amount of heat in an object is measured in an experiment to be ten Joules; so we would write this result as Q = 10J

Temperature, on the other hand, is one of a number of measurements we can make, called thermodynamic variables, of real systems that we study using the laws of thermodynamics.

## Thermodynamic variables

Thermodynamic variables are those properties of a real system which can be observed by simple apparatus on a scale that can be readily understood by human beings. These contrast with statistical variables which by and large are estimations and inferred quantities relevant to the atoms within a material, whose existence is not relevant to macroscopic thermodynamics. At this point we make no hypothesis whatsoever on the nature of the material itself, as the laws of macroscopic thermodynamics are concerned only with large quantities of (usually) homogenous matter.

## States and State Diagrams

When physicists talk about the state of a thermodynamic system, what they mean is that the system has precise or 'well-defined' thermodynamic variables. That is to say, the system's pressure, volume and temperature are fixed at that point in time - we call this an equilibrium state. Only equilibrium states can be studied with basic thermodynamics - states where these variables are not changing at this precise moment in time. If these properties are changing, it no longer makes any sense to say that the system has a particular temperature, because energy will be moving around the system in ways that cannot be precisely measured. Similarly with pressure and volume; these cannot be precisely defined for a changing system because not every particle in the system is 'aware' of their current value, and certain areas of the system may behave as though the system has different pressure and volume.

Therefore, if we want to study a system which we know is changing in time, we must consider it to be a succession of equilibrium states - we pretend that instead of changing smoothly, the system jumps instantaneously between very many slightly different equilibrium states as it goes from its initial state to its final state.

### The state diagram

It follows from the above statements that if a system has precisely defined thermodynamic variables, they can be plotted on a graph. An example, the P-V diagram, is shown below:

Source: Image:P-V_diagram.PNG

Source: Image:RefrigerationTS.PNG

## The Gas Laws

The gas laws are a set of laws that describe the relationship between thermodynamic temperature (T), pressure (P) and volume (V) of gases. It is a loose collection of rules developed between the late Renaissance and early 19th century. Early gas laws were:

• Boyle's law - the product of the volume and pressure of a fixed quantity of an ideal gas is constant, given constant temperature
• Charles's law - at constant pressure, the volume of a given mass of a gas increases or decreases by the same factor as its temperature increases or decreases
• Gay-Lussac's law - the ratio between the combining volumes of gases and the product, if gaseous, can be expressed in small whole numbers

These were combined to form the combined gas law:

${\displaystyle {\frac {P_{1}V_{1}}{T_{1}}}={\frac {P_{2}V_{2}}{T_{2}}}}$

Avogadro's law (1811) surmises that equal volumes of gases, at the same temperature and pressure, contain the same number of molecules. All four laws were generalized into a the simplified ideal gas law:

${\displaystyle \qquad \qquad PV=nRT}$

where:

## The Ideal Gas

The Ideal Gas is a simple model for a gas derived from the gas laws above. The Ideal Gas Equation relates pressure, temperature and volume in all possible combinations for a model gas which has the following properties, making it unlike the 'real' thing:

• The particles in the gas have no size
• The particles in the gas do not interact - that is, they cannot 'bounce off' one another, only the walls of the container, and do not exert any forces on one another

As a consequence of these points, further properties emerge that are still important in themselves:

• The gas never changes phase (never liquefies or alters its properties) and cannot chemically react

The Ideal Gas is described by a single equation:

PV=NRT

Where:

• P=Pressure in Pascals (Pa)
• V=Volume in cubic metres (m^3)
• T=Temperature in Kelvin (K)

N is the number of moles of gas in the volume R is a constant, the Molar Gas Constant. This is not important to know the details of at this stage, except that is approximately equal to 8.31

From this equation, we note that the product PV is directly proportional to T. This tells us the following about the behavior of gases:

• If the temperature of the gas remains constant, either P or V can increase provided that the other decreases by the same proportion; you could double the pressure while halving the volume and not change the temperature of the gas, for example
• If T changes, there are many combinations of P and V that can achieve this. To raise the temperature of the gas you can increase the pressure, decrease the volume, or change both at the same time and achieve the same temperature increase.

We also note that it would in theory be possible to alter the state of the gas by changing the number of particles, N. This is possible, but adding or removing particles involves manipulating chemical potentials, which are part of Statistical Mechanics and rather too complex for this lesson.

### Exercise

Consider a sealed box of gas at atmospheric pressure (300 kPa) and room temperature (293 K). The gas is heated by a flame until its temperature is 400K. Calculate the change in pressure, ${\displaystyle \delta P}$. (Click expand for the worked answer)

## Book list and study hints

Statistical mechanics