The Second Law of Thermodynamics

We've already discussed the First Law of Thermodynamics, the Law of Conservation of Energy. The Second Law is a little more complicated and comes in various forms. The Second Law is a statement that not all processes are reversible. For example, ff you drop an egg, it breaks. It won't spontaneously put itself back together. Or, maybe closer to home, your room won't clean itself. Basically, the Second Law states: Basically, the Second Law states:

“Heat flows naturally from a hot object to a cold object. It will not flow from a cold object to a hot object.”

This leads us into a discussion of a heat engine. A heat engine is an engine that converts thermal energy to mechanical work. The first practical device to do this was the steam engine. In a heat engine, a high input heat (QH) at a high temperature (TH), measured in Kelvin, is transformed in the engine into some work (we'll talk about why only some later) and exhausted as a lower heat (QL) at a lower temperature (TL), also measured in Kelvin. By the Law of Conservation of Energy,

QH = W + QL.

There are some interesting and important points to note. The first is that there is always a temperature difference between the high side and the low side that is required to make the engine run. The driving medium for most engines is steam or hot gases. If there is no temperature difference across the engine, there is also not a pressure difference across the engine and the gases won't flow to do work.

 The second point deals with the efficiency of the engine. Efficiency, e, is the ratio of the work done to the heat input, or

This may also be expressed in terms of the heat in and the heat out as

We can take a look at a third way to express this after we talk about Carnot cycles. The Carnot Cycle, named for Sadi Carnot, is the name given to the most efficient engine cycle possible. In a Carnot cycle, each process was considered to be a reversible process. In reality, this isn't true because of friction and heat losses that cannot be overcome. The four stages of the Carnot cycle are:

  • Gas is expanded isothermally (at TH) with the addition of heat.
  • Gas expands adiabatically. No heat is added, so temperature drops to TL.
  • The gas is compressed at a constant temperature, TL. Heat flows out.
  • The gas is compressed adiabatically. No heat is exchanged, but the temperature
         is raised back to TH.

In a Carnot cycle, the efficiency is determined by the change in temperature, or

For an engine to have 100% efficiency, the exhaust temperature would be 0 K (Absolute Zero). That's not going to happen! This leads us to another definition of the Second Law and a discussion of entropy. Because of the requirement to get the exhaust temperature to absolute zero, we can also write the second law as

"No device is possible whose sole effect is to transform a given amount of energy completely into work."

This is the Kelvin-Planck statement of the Second Law.

Entropy is best defined as a state of randomness. The German Physicist, Rudolf Clausius stated the term along with several other important contributions to thermodynamics. Entropy (S) is a description of the state of a system. It really isn't energy, but is more a measure of the order ( or disorder) of a system. When we talk about entropy, we talk more precisely about the change in entropy (DS) of a system. Specifically,

When heat is added, the entropy of the system increases. Temperature, in Kelvin, is kept constant in order to quantify the entropy. Now, here is the important part. In an isolated system, the entropy of the system never decreases. For any non-ideal process, the change in entropy is always greater than zero. Thus, we have our third statement of the the Second Law:

The total entropy of any system always increases. That is, natural processes will move to a state of greater disorder.

Mathematically, we say

This can lead to some interesting discussions on heat death, the general trend of the universe, and the theories of evolution vs. creation. We'll discuss these more in class.

For more on the Second Law of Thermodynamics, try:

For more on the Carnot Cycle:

And for more on Entropy: (Take some of this with a grain of salt!)

For Practice Problems, Try: Giancoli Multiple Choice PracticeQuestions (All Questions)