Tuesday, December 6, 2011
The development of steam engines during the industrial revolution went hand-in-hand with formulation of one of the most powerful laws of physics. The second law of thermodynamics provides insight into everything from the workings of refrigeration systems and such oddities as black holes to why time only runs forward.
The second law is frequently misunderstood, ignored or misstated to obscure its meaning. Consequently, countless would-be inventors have expended energy in fruitless attempts to build perpetual-motion machines, which the second law demonstrates is not possible.
The second law has many implications that have led to its being stated in a number of ways. Some formulations are rigorous and make reference to an unfamiliar quantity, while others are more pragmatic. Ultimately, they are all equivalent.
One formulation states that, in a closed system, entropy always increases. Entropy is a thermodynamic parameter, like heat and temperature, which is necessary to characterize the thermal properties of a system.
First, one must understand that the thermal energy of a physical object is simply the sum of all the energy of motion, or kinetic energy, of the atoms that make it up. As temperature increases the atoms of a solid vibrate more vigorously. In gases, atoms or molecules fly about at ever higher speeds.
Most things have structure of some kind. Crystals are examples of very regularly shaped objects. The outward appearance of crystals is the result of their atoms being arranged in a repeating lattice.
Imagine an ice cube in a warm room that is otherwise isolated from outside influences. Water ice is crystalline, but, over time, its structure disintegrates. That is, it melts and becomes a liquid.
Water molecules in a liquid state attract one another sufficiently to give the liquid self-adhesion. As a result, though it is less structured than ice, a drop of water takes on a structure tending toward a spherical shape.
Liquid water proceeds to evaporate, becoming a gas. In this phase, water and air molecules behave independently of one another, flying about randomly, colliding and ricocheting off each other.
Eventually, all structure disappears. With the passage of time, water molecules have gone from being in a regular, rigid structure, to a loose aggregation in a liquid, to whizzing about freely in a gaseous form. Ordered states have yielded to progressively more disordered states.
At the start, thermal energy in the room was partitioned. The ice cube, air and walls were at different temperatures. Eventually, everything is at the same temperature.
The thermal energy is now dispersed. Individual atoms or molecules have a range of kinetic energies, but, on average, one region has no more thermal energy than another. Entropy is a measure of the extent to which a system moves from distinctly identifiable regions, that is, displays patterns, to uniformity. It is a measure of the loss of structure or increase in disorder.
Steam engines do work by exploiting temperature differences between reservoirs. A fire boils water in a chamber (hot reservoir). The resulting steam expands, applying pressure and doing work on a piston that drives a mechanism.
Steam, with its residual heat, is vented to the surroundings (cold reservoir) at the end of each cycle. The efficiency of the engine depends on how much heat is available to do work versus heat lost to the surroundings. Losses include those due to friction between the moving mechanical parts.
If the engine were to become a closed system, that is, it was left alone and isolated, the engine's fire would burn out and it would cease functioning. Eventually, like the ice cube example, the entire system attains a uniform temperature. The complex molecules making up its fuel have broken, apart leaving ashes.
To maintain operation the system needs to remain open. A supply of new fuel and the dissipation of lost heat are needed to maintain the temperature difference between the reservoirs.
Suppose an engine in a closed system is used to build a structure. Looking narrowly at a structure built from raw materials one would say order increased, and entropy decreased. However, this is but a small corner of a larger system.
More broadly, taking into account losses in chemical structure of the fuel and lost partitioning of heat reservoirs, the system, as a whole, increased in entropy.
Structure can be built in a closed system. But, to the extent you create order in one location, you create more disorder elsewhere. Entropy can decrease locally, but only at the expense of a larger increase on a broader scale.
The second law was stated more succinctly, without explicit reference to the concept of entropy, by Lord Kelvin in the mid-19th century: No process is possible in which the sole result is the absorption of heat from a reservoir and its complete conversion into work.
In any system there are always energy losses that cannot be used to do work. As a result, you can't build something that does work and at the same time reenergizes the reservoir it draws upon to do that work. Perpetual motion machines are impossible.
Though our solar system approximates a closed system, the Earth does not. Many structures on Earth exist because the planet is an open system. Weather patterns and all of life owe their existence to the Sun providing a continuous supply of radiant (electromagnetic) energy to the planet.
To the extent structure arises on Earth as a result of solar radiation, larger amounts of disorder are created in the Sun. The Sun will eventually burn out, leaving the equivalent of a heap of ash. When that occurs, the Earth will truly be a closed system. The structures the Sun's energy makes possible on Earth will then disintegrate.
The second law is very profound. I have made frequent references to how, in a closed system, a property called entropy increases with the passage of time. This arises because of irreversible processes that take place in the physical world.
The second law affirms that events run forward, not backwards in time. Without work being done a pile of sand on the beach won't spontaneously reassemble itself as a sand castle and liquid water won't spontaneously crystallize as ice. The second law is said to demonstrate the arrow of time, which only fires in one direction: forward.
Steve Luckstead is a medical physicist in the radiation oncology department at St. Mary Medical Center. He can be reached at firstname.lastname@example.org.