# The Zeroth Law of Thermodynamics

Updated on November 17, 2016

Katie graduated with both a BA in Chemistry from BYU and a BA in Spanish from UVU in 2016. She will graduate from medical school in 2020.

## Why Is There a 0th Law of Thermodynamics?

What would later be known as the zeroth law of thermodynamics was first stated in 1787 by Joseph Black. The term zeroth law of thermodynamics first appeared in literature in 1939 and was so named because it was fundamental to understanding the other 3 laws, but hadn’t been formally numbered in the literature as a law before the other 3 laws of thermodynamics.

## Understanding the 0th Law of Thermodynamics

In an isolated system, the total energy remains constant. However, although the total energy remains constant, energy is transferred between bodies and the distribution of rotational, translational and vibrational energy fluctuates as atoms, ions and molecules move and collide. Due to the constant transfer of energy, it is impossible to describe the exact state or instantaneous configuration of a system. The closest we can come to that description is to describe the average number of molecules in each energy microstate, which is known as the average configuration of the system. The number of configurations available to the system is known as entropy and can be calculated using Equation 1.

S=kBlnΩ (Eq. 1)

S is the symbol for entropy; kB is Boltzmann’s constant, 1.3806488*1023 m2 kg s-2 K-1; and Ω is the number of microstates

When the statistics of the possible distributions of energy and microstates are analyzed, one microstate overwhelms the others. The macroscopic properties of the system reflect this microstate. The ratios of the numbers of atoms in each microstate which define the given configuration are given by the Boltzmann distribution. Restated, the Boltzmann distribution defines the most probable distribution of the molecules of a system over their available energy states.

Temperature is the parameter that defines which energy states are occupied by the molecules and is proportional to the average kinetic energy of the system’s constituent microscopic particles, atoms and molecules. Ground temperature is defined as the absolute temperature being 0 K and requires that the lowest energy level, the ground level, is occupied by all particles. Infinite temperature allows all available energy states to be equally occupied.

## The 0th Law Simply Stated

The zeroth law of thermodynamics states that if two systems are individually in thermal equilibrium with a third system they are in thermal equilibrium with each other. It defines the concept of temperature such that the empirical values of the parameter are equal for bodies that are in thermal equilibrium. The movement of thermal energy to reach this thermal equilibrium is defined as heat and is caused by the random collisions of molecules. Heat will always flow down its gradient, from “hotter” to “colder” objects, until thermal equilibrium is reached. This is driven by the system’s tendency to reach maximum entropy, which occurs at thermal equilibrium.

## For Information on the First, Second and Third Laws of Thermodynamics...

You can view information on the First Law of Thermodynamics here and information on the Second and Third Laws of Thermodynamics here.

1

2

12

37

19

8