THD - Second Law of Thermodynamics

Second Law of Thermodynamics

Introduction

The first law of thermodynamics deals with conservation of energy, but just because a situation conserves energy, doesn't mean it will actually happen.

Consider a ceramic coffee cup sitting on a counter. Being above the floor it has gravitational potential energy. If that cup were knocked off the counter it would fall, converting that potential energy into kinetic energy. Once it hit the ground, the cup would use some of that kinetic energy to break internal bonds causing it to shatter. Now you have a broken coffee cup sitting on the floor. On paper, this process could reverse itself. The thermal energy lost during the shattering of the cup could go back into the cup, causing the pieces to mend. The cup could then regain its kinetic energy and fly upwards, landing neatly back on the counter. Mathematically, energy has been conserved.

The second law of thermodynamics explains why some processes can occur, while others do not. A basic interpretation of the second law is that heat can flow from a hot object to a cold object, but never spontaneously from a cold object to a hot object. This works well to explain why your hot cocoa, sitting on the counter always cools down to room temperature instead of pulling in heat from the air to become warmer. This basic interpretation of the second law doesn't, however, do a great job explaining all situations.

Heat Engines

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A heat engine is any device that takes energy from a high temperature reservoir and uses it to do work. In an ideal world the Q into the engine would equal the W out. Since no engine is ideal, some of that energy must be lost. We say the lost heat is exhausted out of the engine to a cold temperature reservoir. Examples of standard heat engines include the internal combustion engine in your car or the steam engines that drove the original railcars. Check out the link in the side bar for a more in-depth explanation of the four-stroke engine.

Consider the simple steam engine. For there to be a net work that can move the piston back and forth, there must be a difference in temperature between the intake and exhaust in the engine. This is an important point with broad implications.

For a heat engine we've seen that

where QH= the heat input from the high temperature source, W = the work done by the engine, and QC = the heat lost to the cold temperature reservoir.

To calculate the efficiency of a heat engine, e:

To get percent efficiency, %e, multiply this number by 100%.

Every heat engine is less than 100% efficient. Most car engines are only between 25-30% efficient. This means that only 70-75% of the energy that goes into them is lost through excessive heat (Why do you think an engine is so hot after it runs?)

To learn about increasing engine efficiency a French scientist, Sadi Carnot, considered an ideal engine (called a Carnot Engine). The cycle of a Carnot engine consists of the following processes:

  1. Isothermal expansion
  2. Adiabatic expansion
  3. Isothermal compression
  4. Adiabatic compression

These processes would allow for maximum, though still less than 100%, efficiency. Carnot found that for his ideal engine, the efficiency was only dependent on the high and low temperatures at either end of the engine. To calculate the ideal (Carnot) efficiency for a heat engine:

This gives the ideal efficiency for any engine. Its actual efficiency will always be less.

Again we see that for work to be done, there must be a difference in temperature, and the energy will naturally flow from high to low temperature. To go against this natural direction, from low to high temperature, requires that you do work on the engine. This is the basis for devices designed to cool objects, like your refrigerator. In order to pull heat from your food and make it cooler, a refrigerators compressor does work on the system to allow the energy to flow from cold to high temperature.

Entropy

So, the natural tendency is for energy to flow from high to low temperatures. If this process takes place through some type of heat engine, the heat flow can lead to work being done. Unfortunately, every time energy flows and transforms from one type to another, it loses some of its ability to do work.

Entropy is the measure of order or disorder of a system. The more disordered a system, the less ability the energy has to do work. This is called a rise in entropy. The total entropy of any system plus that of its environment increases as a result of any natural process. This is the general state of the second law of thermodynamics. Stated simply, natural processes tend to move toward a state of greater disorder. This helps to explain why we don't see our broken coffee cup mend itself spontaneously. That would be a move that would decrease the entropy of the cup.

Every natural process leads to the increase in entropy of the universe. This has long term ramifications that you will discuss in your next assignment.

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