# Thermal Equilibrium: Exchange of Kinetic Energy

• boletoms
In summary: In 2d collisions, the velocities can change in both the x and y directions, so the formulas are more complicated. In summary, in 2D collisions with equal masses, the velocities can change in both the x and y directions, and the law of conservation of energy must still be followed. The formulas for the velocities are: v1=(u2+u1)cos(x/2) and v2=(u2-u1)sin(x/2).
boletoms
as we know that atomic collisions are perfectly ellastic
perfectly ellastic collisions are given by
v1=u1(m1-m2)+2(m2)u2 / m1+m2
and v2=u2(m2-m1)+2(m1)u1 / m1+m2
when m1=m2
v1=u2
v2=u1

we know heat is stored in the form of vibrational energy(kinetic energy)
so to exchange energy they should collide
according to ellasticity the should exchange their energies
T1° will become T2° and T1° will become T2°
the how will they come to equillibrium

Your formulas apply only in one dimension. In one dimension, it is true that colliding particles will not thermalize.

this is just a doubt in ellasticity and not thermodynamics
in 2d collisions
when m1=m2
v1=(u2+u1)cos(x/2)
v2=(u2-u1)sin(x/2) [scource : http://en.wikipedia.org/wiki/Elastic_collision ]
initial total energy(T.E)=1/2(m^2)(u1^2 +u2^2)
final T.E=1/2(m^2)((u2-u1)^2)

according to physics laws initial T.E should be equal to final T.E

hence , 1/2(m^2)(u1^2 +u2^2)=1/2(m^2)((u2-u1)^2)

(u1^2 +u2^2)=((u2-u1)^2)

which is only possible when u1 or u2 is equal to zero
but when u1 & u2 are not equal to zero they violate the law of conservation of energy

why is that so?

Last edited:
Please move this to the Classical Physics forum. This has nothing to do with Quantum Mechanics.

Bill_K said:
Please move this to the Classical Physics forum. This has nothing to do with Quantum Mechanics.

could you tell me how to do it
i'm new to PF

Your formulas do not appear in the wikipedia article that you cite, and they are not correct.

Avodyne said:
Your formulas do not appear in the wikipedia article that you cite, and they are not correct.
look for 2d collisions i just modified the relative initial velocity as u1+u2

and before that please substitute m1=m2

Your formulas are from the 1d section.

## 1. What is thermal equilibrium?

Thermal equilibrium is a state in which two or more objects have the same temperature and there is no net transfer of thermal energy between them.

## 2. How is kinetic energy exchanged in thermal equilibrium?

Kinetic energy is exchanged in thermal equilibrium through the random collisions between particles in the objects. These collisions result in the transfer of energy from faster-moving particles to slower-moving particles, until the objects reach the same temperature.

## 3. What factors affect the rate of thermal equilibrium?

The rate of thermal equilibrium is affected by factors such as the difference in temperature between the objects, the type of material the objects are made of, and the surface area of the objects.

## 4. Can thermal equilibrium be achieved in a closed system?

Yes, thermal equilibrium can be achieved in a closed system as long as there is no external heat source or sink. In this case, the objects in the system will continue to exchange kinetic energy until they reach the same temperature and thermal equilibrium is achieved.

## 5. How is thermal equilibrium important in everyday life?

Thermal equilibrium is important in everyday life as it allows us to control the temperature of our surroundings, whether it's through heating or cooling systems. It also plays a crucial role in processes such as cooking and refrigeration.

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