Chapter 18: Thermodynamics

Literally, Thermodynamics means the flow of heat. Chapter 18 ties together the ideas presented in Chapters 15, 16, and 17 and extends them into a tight package contained in the First Law of Thermodynamics (essentially expressing the Law of Conservation of Energy) and the Second Law of Thermodynamics (the idea that the Entropy of a system stays the same or increases). Entropy is a slippery concept and will be discussed as it relates to the Second Law of Thermodynamnics , the direction of heat transfer, and something known as the Arrow of Time.


First Law of Thermodynamics

The First Law of Thermodynamics concerns the amount of energy in a system and how heat transferred and work affects energies in systems. In thermodynamics we must be careful about what is the system and its surroundings:

The First Law of Thermodynamics is the law of energy conservation in systems. To understand the First Law of Thermodynamics we first consider the ways energy can be stored and ways in which the internal energy can be changed in systems. The First Law of Thermodynamics considers internal energies, heat transfer, kinetic and potential energies, and work. (Note--Work is the amount the kinetic energy of systems change after a force (can be the internal pressure performing work on the outside causing an expansion of the system or an outside force, an external force, that performs work on the system.)


Internal Energy and Kinetic Energy

The coin has two forms of energies. Imagine that we look at the coin. If it sits on a table, it doesn't move but it still has energy. On a microscopic level, the molecules and atoms are moving around (translating) and so have translational energy (leading to temperature) and the atoms and moledules can also have other forms of energy such as rotational, vibrational energies). These forms of microscopic energies are the internal energy of the coin.

If I drop the coin, it can also move. This bulk motion of the material in the coin, is what is referred to as the Kinetic Energy of the coin.

Work

If I apply a force to an object leading to increased motion, work is performed. If the object does not move, then no work is performed, despite the application of a force. Work is when force is applied and movement ensues.

Potential Energy and Kinetic Energy

The Bicyclist has two macroscopic types of energy. When the bicyclist is moving, there is Kinetic Energy. The bicyclist can also have energy, even when stationary. At the top of the hill, if the bicyclist is resting there is no Kinetic Energy. However, the bicyclist does contain energy, Potential Energy. Gravity pulls the bicyclist downward, however, the ground resists gravity's pull on the bicyclist. If the bicyclist is nudged and moved off off the peak of the hill, the pull of gravity becomes readily apparent. The bicyclist starts to move and the Potential Energy is converted to Kinetic Energy.


Adiabatic Changes

In general, most physical systems are complicated with heat flowing into the system or heat flowing out of the system making the determination of how the system's internal energy evolves difficult. There are special circumstances which can arise, however, where one can imagine that heat does not flow into or out of the system. Such systems are Adiabatic and changes in such systems as Adiabatic Changes.

Adiabatic Changes can occur in localized regions of the atmosphere. For example, in parcels of fluid (few tens of meters to a kilometer or so in size), so that as the gas rises or falls, it does not mix with its surroundings, and because they only exist for minutes ot hours, significant heat transfer into and out of them does not occur. In this case, as the parcels of air rise or fall in altitude, they expand or compress in response to the change in altitude (change in local atmospheric pressure) and so cool or heat as they rise or fall.

For dry air, this is a large effect; the temperature of a fluid parcel changes 10 degress Celsius for every 1 kilometer change in altitude. In certain types of geographic locations, this is a huge problem. The Los Angeles basin has air flowing in from the Mojave desert, adiabatically heating as it flows into the LA basin, and cool rising and cooling air flowing in from the ocean. This leads to a Temperature Inversion and a Cold Trap that traps air in the Los Angeles basin:

Non-Adiabatic Changes

The lower level of the Earth's atmosphere, the Troposphere, the layer where convection currents generate weather, behaves roughly as described above. Above the Troposphere, heat is transferred to the atmosphere by the absorption of Solar ultraviolet radiation by Ozone molecules in the Stratosphere and by atoms in the Thermosphere. The heat input leads to high-altitude temperature inversions. The temperature inversion due to the Ozone layer is particularly important.

In the Tropospere, water vapor is free to rise in altitude because of the declining temperature of the atmosphere. However, at the temperature inversion, the overlying gas is warmer and so has lower density than the water vapor which it prevents its further rise. This Cold Trap keeps the water vapor below the Ozone Layer and shielded from the Solar ultraviolet radiation. If the water vapor was exposed to the Solar ultraviolet radiation, it would be broken apart into its constituent atoms, oxygen and hydrogen. The light hydrogen atoms would easily escape the pull of the Earth's gravity and be lost to space. The oxygen would be gobbled in other organic molecules effectively making it impossible for the water to reform. This likely is what happened on Venus.


Second Law of Thermodynamics

The second law of thermodynamics is the statement that heat does not spontaneously flow from a cold object to a hot object or that a system tends to become more disordered with time if left to its own devices.

  • The former statement puts a limit on the efficiency of Heat Engines, machines that convert internal energy to useful mechanical work. Heat engines operate betwen two temperatures, Thot, the T of the initial gas, and Tcool, the T of the waste gas (the untapped energy). Carnot showed that the efficiency of a Heat Engine was given by

    efficiency = (Thot-Tcool)/Thot

  • The latter statement is that the Entropy of a system increases or stays the same if the system is not disturbed.

(We can drive heat flow or change entropy in the opposite senses to those stated, if we perform work on the system.)


Entropy

Entropy is a measure of how disorderd is a system. The Second Law of Thermodynamics says that the Entropy increases or stays the same if the system is not disturbed.

In the simulation, the particles expand to fill all available space ==> went from ordered to fully disordered.

The matter in the Universe is not disordered, the matter has ordered itself into galaxies. Does this violate the Second Law of Thermodynamics?


Entropy and the Arrow of Time

Physics is time-reversible. Although not strictly showing time-reversal, Newton's Cradle (see left) illustrates this idea. The causal sense of time is powerful, but time reversibility suggests there might be issues, that is, what is the correct direction for the flow of time?

We defined the Entropy as a measure of disorder. The Second Law of Thermodynamics states that Entropy stays the same or increases in our Universe (see right). The increase of Entropy offers a natural way in which to define the arrow of time. A cute video of a talk given by Sean Carrol of this notion may be found on Youtube, The Arrow of Time.