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# Law of ThermoDynamics

09th Jan 2022 @ 10 min read

Physical Chemistry

Thermodynamics is an important branch of science that talks about the temperature, work, heat, energy, and entropy of a thermodynamic system. These parameters are governed by the four laws of thermodynamics, which also form the basis of natural sciences and physics.

The four laws are the zeroth law, the first law, the second law, and the third law. These laws are universally valid to any thermodynamic system and are described as follows:

### Zeroth law of Thermodynamics

The zeroth law of thermodynamics states: if two systems are in thermal equilibrium with a third system, then the former two systems are in thermal equilibrium with each other. In other words, if system A is in thermal equilibrium with system C and system B is also in thermal equilibrium with system C, then system A and system B are in thermal equilibrium with each other.

The zeroth law talks about thermal equilibrium and temperature. When we say two systems are in thermal equilibrium, we mean that they have the same temperature. Thus, the temperature of system A, system B, and system C is the same if they are in thermal equilibrium.

Now, in order to justify the zeroth law, we need to measure the temperature of the system. And how do we do that? Well, the simple answer is a thermometer.

Consider the following setup: In the above apparatus, we have three closed systems: A, B, and C.

All three are separated by a wall that allows the exchange of heat with an adjacent system, but no exchange of matter. To rephrase this, heat can pass back and forth from A to B and B to C via the walls, but the content of the system is restricted by the boundaries of the systems.

Now, according to the zeroth law of thermodynamics, if A is in thermal equilibrium with B and B is in thermal equilibrium with C, then A and C are in thermal equilibrium with each other. TA, TB, and TC are the thermometer reading of the respective systems. So, if TA = TB and TB = TC, TA = TC.

### First law of Thermodynamics

The first law of thermodynamics is a more meaningful and practically useful law. There are some variations in the statement of the law. One of the statements is that energy can neither be created nor be destroyed but can be transformed from one form to another. This statement may sound similar to the law of conservation of energy.And indeed, they are the same. You can say the first law of thermodynamics is a version of the law of conservation of energy.

In thermodynamics, we have the system and its surroundings. The system is defined as a confined space with certain characteristics. It can be isolated, closed, or opened. And the surrounding is the rest of the universe other than the system.

The sum of the energy of the system and surrounding is always constant and equal to the energy of the universe.

Esys + Esurr = constant = Euniv

We can revise the previous statement to be more specific for thermodynamics: The energy of the system can be converted from one form to another through heat, work, or internal energy.

The change in the internal energy of the system (ΔU) can be given by

ΔU = Q + W + ∑mU

Here, Q is the heat exchange between the system and surrounding. If net heat flows into the system from the surrounding, Q is a positive value. And Q is a negative value if the net heat flows out of the system to the surrounding.

W is mechanical work done. W is a macroscopic quantity and it is a positive value if the surrounding performs external work on the system, for example, the compression of the system. Work done is a negative value if the system performs work on the surrounding, for example, the expansion of the system.

∑mU is the flow of internal energies in the form of matter transfer. m is mass transfer and U is internal energy per unit mass.

For a closed system, the matter transfer across the system’s boundaries is zero. So, ∑mU = 0. Thus, we can rewrite the above equation as:

ΔU = Q + W

Also, mechanical work is the work done by the system or upon the system against external pressure P. So, W = −PΔV. ΔU = Q − PΔV

We can articulate the above equation in words: For a closed system, the change in the internal energy of the system is the sum of heat transfer and mechanical work.

### Second law of Thermodynamics

The second law of thermodynamics is about entropy and spontaneity. It says the total entropy of the interacting thermodynamic systems never decreases. The increase in the total entropy signifies the spontaneity of the process. And if the total entropy remains constant, it means the process is at thermodynamic equilibrium.

Another primitive version of the law is heat does not spontaneously flow from a colder system to a warmer system.

Almost all things around us are spontaneous and irreversible, for example, falling of water from a height, breaking of glass, or bursting of crackers. All the activities that you are experiencing around you are spontaneous and cannot be reversed. When I say cannot be reversed, I mean we cannot restore a system and its surroundings to the original state. For example, glass that is broken is broken. None can bring the glass and the rest of the universe to its original thermodynamic state.

The irreversibility of all things in the universe means the entropy of the entire universe, as an isolated system, always increases.

The change in entropy of a closed system is given by ΔS = Q/T + Ṡ.

Here, Q is heat flow into the system, T is the temperature of the system, and Ṡ is the entropy production inside the system.

For an isolated system, Q = 0, so ΔS = Ṡ.

And for a reversible system, Ṡ = 0, so ΔS = Q/T.

### Third Law of Thermodynamics

The second law talks about the concept of entropy in a system, but it does not quantify entropy. The third law allows us to calculate the absolute value of entropy. It states for a 100% crystalline system, the absolute value of entropy at absolute zero temperature is always zero.

If a system is non-crystalline, the entropy will be a finite value but smallest at absolute zero. Entropy is an indication of randomness or disorder in a system. As a system approaches absolute zero, all the processes (disorders) in the system cease and consequently, the entropy reaches its minimum.

A mathematical expression can be derived using statistical mathematics: S = k ln Ω.

Here, k is Boltzmann’s constant and Ω is the number of micro-states.

For a 100% crystalline system at absolute zero, the number of micro-states equals one. So, S = k ln (1) = 0.

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