Thermodynamics


...is the study of heat in physics.

The industrial revolution

Throughout most of our history the main sources of energy at our disposal were human and animal

But starting in 17th century Britain, there was a technological explosion of creating machines/engines powered by coal to do work for us.

1712 - One of the first practical engines was Thomas Newcomen's which was used to draw water up from coal mines.

  1. A coal fire heats water to boiling.
  2. Steam fills the cylinder.
  3. Steam valve closes.
  4. Cold water sprayed onto the cylinder causes the steam vapor to condense to water, creating a vacuum in the cylinder.
  5. Vacuum pulls piston & left side of beam down.
  6. Right side of beam pulls up weight attached below-ground.

Carnot

1824 - Réflexions sur la Puissance Motrice du Feu ("Reflections on the motive power of fire"), Sadi Carnot came up with an abstract way of thinking about the steam engines of his time--as a heat engine:

Any machine which converts some heat (generated by burning coal, gas, oil; or a nuclear chain reaction; ...) into mechanical energy.

He asked:

  • Is the work available from a heat source potentially unbounded?
  • Can heat engines in principle be improved by replacing the steam with some other working fluid or gas?

He pictured heat as a material substance--"caloric"--falling from high temperature to lower temperature--much like falling water powering a water wheel--and concluded that the greater the temperature difference, the more mechanical work could be done.

Joule's experiment

1845 - James Joule made difficult measurements of the temperature increases of water in relationship to the change of mechanical energy of falling weights

...which started to convince people that heat is a form of energy, and paved the way for our modern understanding of...

Conservation of Energy

Much of analytical mechanics and general physics can be summed up by the law of conservation of energy:

The total energy of all the participants in any process remains unchanged through that process. That is, energy cannot be created or destroyed.

Energy can be transformed (changed from one form to another):

  • Chemical energy,
  • Gravitational potential energy,
  • Nuclear energy,
  • Heat,
  • other forms...

Energy can be transferred (moved) from one body to another,

...but the total amount always remains the same.

The idea of conservation of energy has been hugely successful. Here, for example, is the story of the prediction and discovery of a completely unknown particle (the neutrino).

But what *is* energy? It's not exactly a material substance...

Beyond energy conservation

Joules' results can be expressed in terms of energy. If we say that the mechanical work done by the falling weights, $\Delta W$, was converted into an equal amount of energy in the form of "heat", $\Delta Q$, then there is an equation that relates that heat energy to a change in temperature, $\Delta T$:

$$\Delta W \rightarrow \Delta Q = m c_P \Delta T$$ where the "heat capacity" of water, for example, is $c_P$=1 cal/gm/${}^o$C.

But now consider the following experiment with water:

  • equal amounts of water, at different temperatures,
  • Put in "thermal contact" at $t=34$ sec.
  • Final temperature of each container of water is halfway between their initial temperatures.

Energy conserved.

  • Think of same experiment...
  • Final temperature of each container of water changes by the same (but opposite) amount.

Energy conserved.

But this scenario never happens in nature...

$\Rightarrow$ Something more than just energy conservation is needed to describe the patterns we see in nature.

This led, eventually, to the second law of thermodynamics which involves entropy -- a concept named only in the 19th century.

Thermodynamics and Statistical Mechanics

Both Thermodynamics and Statistical Mechanics cover the ground that we're interested in:
ThermodynamicsStatistical Mechanics
  • ...a phenomenological theory of continuous matter,
  • macroscopic variables like volume, pressure, temperature, magnetization.
  • ...a microscopic, atomic theory,
  • microscopic variables include individual atomic positions, velocities, spin

But the two theories are connected. We'll find eventually, for a system of idealized, billiard-ball like atoms of mass $m$, that the temperature of the system (a macroscopic variable) is related to the average kinetic energy of atoms (a microscopic variable): $$T \propto \frac{1}{2}mv_{\rm rms}^2.$$

From a practical engineering point of view, thermodynamics is attractive, since you don't have to keep track of $10^{20-50}$ variables.

But, we'd like to explain things in terms of more fundamental quantities: Statistical mechanics makes the connection between the "average" quantities of thermodynamics and the microscopic characteristics of atomic particles.

Image credits

Flickr users Omegaman, mdavidford, Taccola wheel, Mostafa Zamani, NASA/CXC/SAO