Simplified Thermodynamics

Thermodynamics is an applied science used in several branches of engineering, including mechanical and chemical engineering. At its simplest, thermodynamics is the study of energy, its use and transformation through a system. Typically, engineering thermodynamics is concerned with changing energy from one form to another. As an example, automotive engines convert chemical energy (enthalpy) from the fuel into heat, and then into mechanical work that eventually turns the wheels.

Thermodynamics principles are used by mechanical engineers in the fields of heat transfer, thermofluids, and energy conversion. Mechanical engineers use thermo-science to design engines and power plants, heating, ventilation, and air-conditioning (HVAC) systems, heat exchangers, heat sinks, radiators, refrigeration, insulation, and others.

Laws Of Thermodynamics (Simplified)

1. Energy cannot be created or destroyed. In other words, in a closed system, the total amount of energy that can be taken out of the system will be equal to the total amount of energy that was put into the system.

2. In any given exchange of energy, there will always be energy lost. This is referred to as entropy. This basically means that in any system, energy will always be lost in some means, be it friction, or some random quantum effect. This also implies that there can be no such thing as a perpetual motion machine as energy will always be lost in some form.

Note that this lost isn't mean to say "destroyed". It rather means unusable. That lost energy is transfered to the microscopical degrees of freedom of the system, as are molecular vibrations, place in which we call it "heat".

3. No system can reach absolute zero temperature. This is due to the fact that at absolute zero, a system has no energy, and thus does not move. Although this does not cause any problems in the sense of classical mechanics; it does cause problems on the quantum level. If a particle had no movement at all, its speed would be exactly known (zero, exactly), which is forbidden by Heissenberg's uncertainty principle.

Engineering is an area in which mathematics is applied to actual real world problems. The basic fundamentals of Engineering all require Calculus to understand. The more advanced topics require knowledge of both ordinary and partial differential equations. Actual applications require the usage of multiple forms of mathematics in tandem with each other. Frequently, multiple partial differential equations are solved at the same time. To solve these equations effectively, a combination of linear algebra and differential equations is used.

One example is in solving the gas equation in chemistry. Standard equations of the "ideal" gas law is PV=nRT. Engineers understand that the "ideal" gas does not exist in reality, and a compression ratio must usually be used. As such the equation is often used as "PV=znRT" where z is used as a compression ratio.

The compression ratio though is a mathematically derived constant which is based on experimental data. The data is taken and has curvefitting applied to it. Basic algebraic curve fitting does not do an adequate job, so a differential approach is applied to it. In order to do this Maxwell's equations must be applied to get the ideal Gas law into a partial differential format.

One of Maxwell's equations is:

                                                     T=(dh/ds)

Where T is temperature, h is enthalphy, s is entropy, and p is pressure.

So, in essence, the temperature is equal to the change in enthalpy with respect to the change in entropy, assuming that pressure is constant. The operator states that the enthalpy (h) is dependent on multiple variables (s,p) and that s is just one of them. By making pressure a constant, the derivative of h just depends on s, and not on p.

By making substitutions like this into the ideal gas equation, the compression factor "z" can be determined for each gas.

Thermodynamics (from the Greek thermos meaning heat and dynamis meaning power) is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics.

Heat is something that is observed by everyone. Warmth and coolness, combustion and oxidation - but Modern thermodynamics is concisely the understanding that heat is the result of the motion of molecules.

Thermodynamics became the unification of the concept of heat with the motion of molecules from investigations of the problem of how to increase the efficiency of early steam engines. It resulted in the understanding of statistical principles of molecules that are profound.

For the purposes of an instructive text, it will be useful to study story of efficiency in heat engines along with examples from physical chemistry in parallel.

The Heat Engine

It turns out that all engines and many other devices that do work are also heat engines. That is they can be seen as functioning by transferring heat from one place to another or generating heat while generating heat.

It not only turns out that engines are the subject of thermodynamics, but also chemical reactions too.

A Simple Steam Engine

To get started, we will focus only on steam engines and see that modern thermodynamics can be seen from this example.

We'll start with a steam engine designed to pump water. You have a closed vessel of water over a flame - when the water boils, steam is produced and goes from the water vessel through a hose to a cylinder. When the steam expands into the cylinder, it will push the cylinder along from a closed to open position, from a small volume to a larger volume.

We'll put a stick on the end of the cylinder and use that to turn a wheel on a pump to pump the water. When the cylinder has gone to its furthest open position (i.e. it has expanded enough) we'll also have the wheel release the steam and push the cylinder back to its starting (or closed) position, close the valve and allow more steam to come in, we need the momentum of the wheel to close the piston. When the piston has returned to its original position, the valve moves to allow in more steam and the cycle starts again.

Looking at this arrangement, we can see that what is driving the piston is the hot steam. When the steam is hotter, the piston will drive with more force and pump more water.

The reason that this engine works is the difference in the temperature of the steam to that of the outside world. We often forget that if the temperature outside the piston were the same as inside,

A Combustion Engine

Chemical Thermodynamics

The Four Laws of Thermodynamics

Conservation of Energy

Heat is a form of energy and energy is conserved. This may seem obvious to some of us - Because heat can come from chemical reactions, like the flame from combustion, it can appear to come from nowhere.

Entropy

The spontaneous flow of heat from one body to another always goes in the same direction, from warmer to colder bodies. When we understand that heat is the result of molecular motion, we can express the flow of thermal energy as the expansion of entropy.

Zero Temperature

A profound result of the understanding of thermal energy as molecular motion is that there is a condition where there is minimal molecular motion (zero point motion), known as absolute zero. However, owing to the uncertainty principle, a molecule will never be absolutely still.

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.

Temperature

Pressure

Volume

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: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:

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:

where:

• P is the pressure in pascals
• V is the volume in cubic metres
• n is the number of moles of gas
• R is the ideal gas constant (8.3145 J/(mol K))
• T is the temperature in kelvins.

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.

Exercises

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, . (Click expand for the worked answer)