Episode 605: The first law of thermodynamics

An introduction to thermodynamics.

Summary

  • Discussion: The First Law and energy conservation (15 minutes)
  • Discussion: Understanding the equation (15 minutes)
  • Demonstrations: Expanding and compressing gases (20 minutes)
  • Discussion: Adiabatic and isothermal changes (10 minutes)
  • Student questions: On the second law (20 minutes)

Discussion: The first law and energy conservation
It is very easy to trivialise the ideas here and forget just how important thermodynamics has been in the development of physics. It is often worthwhile exploring this issue from two angles.

The first is historical and the following brief outline should serve as the basis for further study: In the late 18th century Benjamin Thompson (Count Rumford) asserted that heat was not a fluid (caloric) stored within materials but was associated with motion in some way. This was deduced from seeing that apparently limitless amounts of heat were generated when boring a cannon, especially as the drill became blunter. However, as this predates a good knowledge of atoms and molecules it is unclear what is moving. In the early 19th century James Joule performed quantitative measurements to compare the amount of mechanical work and heat that would raise the temperature of a known quantity of water by the same amount. This is the basis of the first law of thermodynamics. Recognition is also given to Julius Mayer, a physician, who noted on trips to the tropics that sailors’ venous blood was redder than when in colder climates, and so contained more oxygen. He deduced that, in the hotter climate, less energy was needed to keep warm and so less oxygen was used from the blood. He was able to link this to the amount of food needed and so made major headway in our understanding of work and energy.

The second approach is more philosophical. Students have had the idea of conservation of energy drilled into them from an early age but few question why we believe it. Ultimately it rests on experiment and there were at least two occasions in the 20th century when the advent of quantum theory and the discovery of new particles made even top scientists question the validity of the law at a level of atoms and below. The first instance involves Compton Scattering, where light scatters off an electron and changes energy and momentum. In the early versions of the quantum theory, conservation of energy and momentum did not seem to both hold at the same time. Even Niels Bohr was willing to sacrifice conservation of energy. It turned out, of course, that the problem lay in the old quantum theory. A second example comes later in the century. In beta decay the beta particle can carry off a variable amount of energy and some appears to be lost. Again scientists were willing to conclude that energy is not conserved at a microscopic level. However, the discovery of the neutrino restored the energy balance.

So what does the First Law say? In words, the internal energy of a body (such as a gas) can be increased by heating it or by doing mechanical work on it. In symbols:

DU = DQ + DW

Compressing a gas with a piston

Note that internal energy U and thermal energy Q are quite distinct concepts. Many text books tend to imply that ‘heat’ (i.e. thermal energy) and internal energy are equivalent.

The sign convention here is that if DU is positive the amount of internal energy increases. This means that DQ stands for the heat energy put into the system and DW for the work done on the system. This is known as the ‘physicists’ convention’. You may come across text books that use the ‘engineers’ convention’. Heat energy put into a system is positive, and the work output is also taken as positive. Providing you are consistent which convention you apply, all will be well.

Episode 605-1: Thermodynamics (Word, 47 KB)

Internal combustion engine

Discussion: Understanding the equation
Practise using the equation and sign convention. Ask what happens to the internal energy as a gas is compressed or if it expands against an external pressure (such as air).

To compress a gas, you have to do work on it. This transfers energy to its particles, so they move faster – the gas is hotter.

If a gas expands against the atmosphere, it must do work to push back the atmosphere. Its particles lose energy and move more slowly, so its temperature falls.

How would such changes be observed? That is, what does a change in U represent? Note that it affects not just temperature but also possibly the state of a gas.

Demonstrations: Expanding and compressing gases
There are a number of possible demonstrations of the First Law. Simple and dramatic ones include commercial devices that let you compress a cylinder of air rapidly and ignite a small wad of cotton. A more conventional alternative is to compress the air in a bicycle pump and to observe the rise in temperature.

Episode 603-1: Warming up a gas by speeding up its particles (Word, 46 KB)

The reverse effect is to demonstrate the formation of dry ice from a CO2 cylinder, letting the gas expand against air pressure. You will need to consult the relevant safety documents for this.

Episode 605-2: Formation of dry ice from a CO2 cylinder (Word, 79 KB)

Mechanical equivalent of heat apparatus

You may also have the equipment for a quantitative analysis. This usually involves a friction drum or wheel and compares mechanical work done against a friction force to the rise in temperature of the system. An alternative system allows mechanical work to be compared with energy supplied electrically.

Episode 605-3: Doing mechanical work (Word, 48 KB)

Episode 605-4: Mechanical and electrical heating (Word, 50 KB)

Discussion
If your specification requires it you could then go on to look at examples of adiabatic changes (in which no heat energy flows in or out – either an insulated system or one, like the bicycle pump, where the change is fast), isothermal changes (where the temperature is kept constant, so DU is zero, usually involving a heat bath to extract or supply heat energy) and constant volume or isochoric (so no work can be done, but heat energy can flow in or out).

This simulation of an adiabatic change may be useful, but beware the different notation used for internal energy: Boston University Physics Department

Student questions
The conservation of energy underlies our modern understanding of physics but also has important implications for our use of energy resources. In particular, the idea that mechanical energy is readily converted to heat energy that can be dispersed is a very practical issue. With little quantitative work in this section, students could be set questions on sensible use of energy resources or the mechanics of power stations. Try to get them to emphasise the difference in meaning between ‘conserving energy’ as in not wasting it and the scientific meaning of conservation.

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Episode 605: The first law of thermodynamics (Word, 216 KB)