The Second Law of Thermodynamics


Second Law of Thermodynamics: Heat naturally flows from high temperature to low temperature but not the other way around; Disorder, or entropy, generation is always positive in a closed system undergoing an irreversible process.

A cycle is defined in a P-V diagram as a system that has a start and an end that are the same point, therefore the pressure and volume may change through out the cycle but will ultimately come back to the starting point. A proposed cycle based on the zeroth and first laws of thermodynamics may be possible naturally, so the second law of thermodynamics was developed to further define when a cycle will occur.

The 2 primary cycles that studied in thermodynamics is the heat pump cycle (refrigerator) and the heat engine cycle. In each case, there is:

  1. Heat entering the system

  2. Heat leaving the system

  3. Net work produced by the system

The most famous is the Carnot cycle, a theoretical limit to the thermodynamic cycle between constant temperature reservoirs. Think about this for a moment, a standard heat engine or refrigerator is using heat to produce work, or work to produce heat.

How does heat produce work? If you think about a piston in a combustion engine, gas is released into the piston chamber, the piston then compresses the air and gas inside the chamber, the gas is ignited from the spark plug and rapidly heats up, the rapid heat increase and expansion due to excitement of particles causes the piston to move up. The expansion caused by the increase in heat and the excitement of particles moves the piston and creates work.

The second law of thermodynamics states that heat as a form of energy flows from hot to cold, but not the other way around naturally.

Think about 2 boxes (box A and box B) touching each other along a single uninsulated boundary, and all other sides of the boxes are perfectly insulated. Box A is at a temperature of 5 degrees C and box B is at a temperature of 10 degrees C. As the excited particles hit the uninsulated boundary, the excited particles in box B will transfer heat energy to the particles in box A until a thermal equilibrium is reached. The particles in box A will not naturally transfer heat energy to the particles in box B naturally.

Carnot Cycle

Let’s back up a bit and take a closer look at exactly what the Carnot cycle is. It is known that a heat engine and a heat pump move heat from a high or low temperature reservoir to a high or low temperature reservoir, producing work or requiring work respectively. These reservoirs are assumed to always be at a constant temperature no matter the amount of heat transferred between the two.

The Carnot cycle operates with these constant temperature reservoirs and every process is completely reversable. Named after Nicholas Leonard Sadi Carnot, the cycle is the most efficient heat engine or heat pump possible.

The Carnot cycle is always made up of these four processes – most easily viewed on a P-V diagram:

  1. A reversable isothermal process

  2. A reversable adiabatic process

  3. A reversable isothermal process

  4. A reversable adiabatic process


Going back to the example of the 2 boxes touching each other. If the barrier is removed, allowing the gas particles to mix together in a closed system, the particles will continuously move and the system will almost never be in the same state on a micro scale (including particle position and velocity).

In a closed system such as this, it has been determined that the disorder of particles within the system will always increase and will not decrease naturally. The second law of thermodynamics can be thought of in terms of entropy by stating that in a completely reversible process and cycle, the entropy (or disorder) generation is zero, but in an irreversible process, the entropy (or disorder) generation is positive.

More generally, the chaotic disorder of the particles in the box and the probability that the particles will not be ordered is correlated with the entropy of a system. Lets say there are 1030 different possibilities for position and velocity of every particle in the box. If the particles are scattered every where and moving at different speeds in different directions, there is a high entropy in the system. If the particles all end up ordered along one side of the box moving in the same direction, there is a low entropy in the system. It is extremely unlikely the particles will become ordered because there are far more possibilities of disorder in the system.

The different possible configurations of the state of the particles is called the thermodynamic probability (w) and is the value of all possible configurations – each given equal weight.

Now that this correlation between entropy and disorder has been discussed, let’s look at the equation for entropy:



k = Boltzmann’s constant = 1.38064852 x 10^-23 J/K

w = thermodynamic probability value (changes based on the number of possible configurations of state

Jarrett Linowes
Mechanical Engineer

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