Why Does the Entropy of a Gas Increase When it Expands into a Vacuum

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Entropy is Disorder. And Gas Becomes More Disordered in Vacuum. 

To be technically correct, entropy is not just a disorder but a measure of disorder. In order to understand, we first have to go through the some basic definitions of thermodynamics and then when I will connect individual ideas presented in this blog under the summary section, you, dear reader, will have a clear understanding of why does the entropy of a gas increase when it expands in vacuum? Let’s start.

Thermodynamics

Thermodynamics is the study of movement of heat energy. Now, in order to study the movement of heat, scientists have come up with a method to differentiate between which movement of heat is under observation. The things which make up the observation part is called the system and anything else is called the environment. So, thermodynamics becomes the study of motion of heat between the system and the surroundings. And this study of motion is governed by four laws, known as the laws of thermodynamics

The Laws of Thermodynamics

The four laws of thermodynamics are empirically proven to be true and will remain so till the end of times. The laws start from the ‘zeroth’ law of thermodynamics and go onto the first, the second and the third law of thermodynamics, totally four laws. The reason behind the start of the numbering of the laws from zero is that, the zeroth law was taken to be so self obvious that nobody bothered to give it a number. By the time the collective scientific community realized its mistake, it was too late to name it the first law of thermodynamics as the real first law of thermodynamics by then was fairly established in the scientific literature.

Zeroth Law of Thermodynamics

The zeroth law of thermodynamics states that if a body A is in thermal equilibrium with a body C and another body B is also in thermal equilibrium with body C; bodies A and B are in thermal equilibrium with each other. In simple english, it just means that if body A has the same temperature as body C, and then body B has the same temperature as body C, then body A and B, also have the same temperature.

Heat and Temperature

A body has a temperature equal to the sum of average kinetic energy of all its atoms and molecules. Heat is  not something which is stored in any body. It is just the rate of flow of temperature from the hot body to the cold body. The greater the temperature difference between the bodies, the greater the heat in the system (remember, now both the bodies are under observation).

First Law of Thermodynamics

The first law of thermodynamics is simply a law of conservation of energy. It means that the total heat energy of the system can neither be created nor be destroyed. It just changes its form from heat to other forms or vice versa. First law deals with the quantity of energy.

Second Law of Thermodynamics

The second law of thermodynamics states that not all energies are equal. Some forms are better than others. Work is a superior form of energy than heat. We can use work to generate heat. But it would be far better to somehow come up with a way to convert heat energy into work. Second law deals with the quality of energy.

Third Law of Thermodynamics

The third law of thermodynamics explains the concept of entropy. It states that at absolute zero temperature (0 on the kelvin scale or -273.16 deg on celsius scale) the entropy of any system is a constant,known as boltzmann constant.

Temperature and Absolute Zero

As described earlier, temperature is the sum of average translational kinetic energy. When we start to decrease this movement of atoms and molecules, the associated kinetic energy also lessens resulting in lower temperature. This process can only go so far before there is no translational movement. That theoretical point (absolute zero can never be achieved in reality) is absolute zero. The translational movement may become zero, but the rotational and vibrational movement is still there.

Entropy and Disorder

In order to know the state of matter, one only needs to look at its entropy. A solid has less entropy than liquid and a liquid has less than gas. Because, in solids, the molecules are jam packed; in liquids they have somewhat independence and in gas, they will occupy any and all space given to them. So, gases are more disorderly than liquids, which in turn are more disorderly than solids. One can easily predict the individual microstate of solid and can assume it to be the same all through it. With liquid, the number of microstates increases. You can guess fairly but the molecules in liquid state have more independence to arrange them in more freely. Enter the gaseous state, the number of microstates increases exponentially, leading to a very high entropy.

Question of the Blog

The question with which we started our blog was why does the entropy of a gas increase when it expands into a vacuum?. Now, with all the information provided above, we can safely answer it.

The bonding force in gas is low and their molecules move freely in their container space, rarely bumping into each other. That is quite a disorder compared to the same molecules in their solid form, where they are right next to each other and cannot move much at all, save for some oscillation around their fixed place. Solids absorb heat and change to liquid and further heat causes them to become gas.

Take the example of water. It is ice at 0 degrees. Liquid between 0 and 100 degrees and gas above 100 degrees. If a lid is provided to contain all the steam inside the container, one can assume quite a disorder of molecules in there. Now, if all of a sudden they were allowed to enter a bigger container, surrounding the first one, with a vacuum in it, one can only imagine the individual number of microstates the gaseous molecules could take in the new space. The more such microstates are, the higher the entropy.

Summary

Entropy is the measure of disorder in the system. The degree of disorder is measured by the individual number of microstates within the system. Each microstate is in harmony within itself. But it is different from other microstates of the system. The higher the number of such microstates, higher is the entropy. So when gas is allowed to expand into a vacuum, its entropy i.e the number of microstates of the total molecules of gas, increases manifold as compared to its normal gas phase entropy (number of microstates).

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