Thermal equilibrium occurs when two substances in contact stop exchanging heat energy and reach the same temperature. This happens because heat naturally flows from hotter to colder substances, increasing the temperature of the colder substance until they are the same. The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third system, they are also in equilibrium with each other. When thermal equilibrium is reached, the substances have equalized their microscopic kinetic energies such that heat no longer flows between them.

1. Thermal equilibrium

2. Contents
What is thermal equilibrium?
Why does thermal equiibrium occur?
Zeroth law of thermodynamics
Second law of thermodynamics
Helmholtz free energy
Mechanical equivalence of heat
Difference between temperature and heat

3. What is Thermal equilibrium?
The condition under which two substances
in physical contact with each other
exchange no heat energy. Two substances
in thermal equilibrium are said to be at the
same temperature

4. Why does Thermal equilibrium
occur?
It is observed that a higher temperature object which is
in contact with a lower temperature object
will transfer heat to the lower temperature object. The
objects will approach the same temperature, and in the
absence of loss to other objects, they will then
maintain a constant temperature. They are then said to
be in thermal equilibrium. Thermal equilibrium is the
subject of the Zeroth Law of Thermodynamics.

5. Zeroth law of thermodynamics
The "zeroth law" states that if two systems are at the same
time in thermal equilibrium with a third system, they are
in thermal equilibrium with each other.

6. Zeroth law of thermodynamics
 There are underlying ideas about heat associated with the zeroth law
of thermodynamics, and one of those ideas was expressed
by Maxwell as "All heat is of the same kind." If A is in thermal
equilibrium with B, then every unit of internal energy that passes
from A to B is balanced by the same amount of energy passing from
B to A. This is true even if the atomic masses in A are different from
those in B, and even if the amount of energy per unit mass in A is
different because the material has a different specific heat. This
implies that there is a measurable property that can be considered to
be the same for A and B, a property upon which heat transfer
depends. That property is called temperature.

7. What happens to the flow of energy if
thermal equilibrium is met
 Temperature is the average kinetic, or movement, energy of
the molecules in a substance. When you put two objects of
different temperatures in contact with one another, the faster-
moving molecules in one material will collide with the slower-
moving molecules in the other. The heat energy will gradually
spread out until the two objects have the same temperature -
until they have reached thermal equilibrium. This is basically
the same as the second law of thermodynamics, which
states that heat only spontaneously moves from hotter places
to colder places, never the other way around.

8. Second law of Thermodynamics

9. Helmholtz free energy
If an object (or system) is in thermodynamic equilibrium, then it
can be said that the system has minimized its thermodynamic
potential. There are many types of thermodynamic potential
quoted in physics, but perhaps the most common one is
the Helmholtz free energy, which measures the total amount
of useful work that could be extracted from the system. The
equation for Helmholtz free energy is as follows:

11. Mechanical equivalence of heat
As we have seen in the zeroth law of thermodynamics,
when two objects are placed in contact heat (energy) is
transferred from one to the other until they reach the same
temperature (are in thermal equilibrium). When the
objects are at the same temperature there is no heat
transfer.
Since heat is a form of energy it can be measured in
Joules. Historically, since heat was believed to be a
separate form of energy, thermodynamics was developed
using a unit of energy unique to heat - the calorie. The
relationship between Joules and Calories is known as
the Mechanical Equivalence of Heat,
1 Calorie = 4.184 Joules

12. TEMPERATURE
 The temperature of a system is defined as the average energy of the
microscopic motions of the particles, atoms, or molecules in the system.•
 In a solid, these motions are primarily the vibrations of the atoms about
their location in the solid.
 •
 In a monatomic gas, the microscopic motions are the translational
motions of the gas atoms.
 •
 In a multiatomic gas, the vibrational and rotational motions of the atoms in
the molecules are also included with the translational motions

14. HEAT
 It has been observed that when a higher temperature object is in contact
with a lower temperature object, heat will be transferred to the lower
temperature object.•
 The objects will reach the same temperature.
 •
 If there is no loss of heat to other objects, the two objects will maintain a
constant temperature.
 •
 The two objects are then said to be in thermal equilibrium

16.  You have two pots of water sitting on a stove. In one, the water is
moving about, tumbling, and bubbling. In the other, the water is still.
Which is boiling?
 From common experience we know that as we heat water it begins to
move, tumble, and bubble; this is the state we commonly call boiling.
This familiar observation lies at the heart of understanding
temperature and heat. Temperature is a measure of the average kinetic
energy of atoms and molecules in a substance. Heat is the flow of this
kinetic energy from one body to another.
 As the water in the pot is heated, its molecules begin to move more
rapidly; once it is boiling, this increase in motion becomes visible as
the tumbling and bubbling we see.

18. Reference
 https://www.webassign.net/question_assets/eraucolphysmechl1/lab_5_1_intro/man
ual.html
 https://www.yourdictionary.com/thermal-equilibrium
 https://www.dictionary.com/browse/thermal-equilibrium