# The laws of thermodyanmics

karthik · updated · flag

Due to some laggy historical enlightenment, the laws of thermodynamics start with zero.

## Zeroth law - Observational definition of temperature¶

When two objects A and B are in thermal equilibrium independently with another object C, then objects A and B will be in a thermal equilibrium with each other. And the temperatures of A, B, and C will be the same. Mathematically, if A = C and B = C, then A = B.

So what this laws states is that, if multiple systems are in a thermal equilibrium, then they all share the same temperature.

## First law - Conservation of energy¶

Energy can neither be created nor be destroyed and can only be transformed to a different form.

In other words, it means that if you have a system with an internal energy of $U_{system}$ in a surrounding that has an internal energy of $U_{surrounding}$, then you can only transfer the energy in and out of the system by adding or removing heat or doing work on the system or surrounding, but can never create new energy or destroy the energy out of existence. Mathematically it’s expressed as follows.

$$\Delta U_{system} = -\Delta U_{surroundings}$$

## Second law - Law of entropy¶

Heat spontaneously flows from warmer system to a colder system to attain a thermal equilibrium, thereby increasing the entropy over time.

The second law states the fact that the change in heat over time smooths out the energy distribution (this is called as the entropy) and makes it so that no usable energy can be attained to do work. As energy is conserved, the entropy just increases.

## Third law - Absolute zero¶

When the temperature of a system reaches absolute zero 0 K, for a perfect crystal, the entropy reaches 0.

Entropy, simply put, is the number of ways the molecules in a system can be rearranged at a given temperature. If there are more ways (when the system is hot), we call it high entropy and vice versa. So when you cool down a perfect crystal to the lowest possible temperature, absolute zero 0 K, the entropy of the system will reach 0.

But due to the Uncertainty principle, a system at absolute zero would still have some internal energy (zero-point energy) and entropy could never be zero. So the third law can be restated as ‘Reaching absolute zero is impossible’.