THERMAL EQUILIBRIUM

• We use the term equilibrium when the temperature of the two systems is equal
• For thermodynamics equilibrium, the system should be in Mechanical, Thermal and Chemical Equilibrium
• If the temperature within the system is unformed and temporally stable, the system is said to be in thermal equilibrium
• The system is said to be in thermal equilibrium if there is no net flow of thermal energy between them, when they are connected by a path permeable to heat
• Systems in thermodynamics equilibriums are always in thermal equilibrium, but the system in thermal equilibrium is not always a thermodynamic equilibrium
• In thermal equilibrium, there may be energy transfer in the form of internal power, but matter and energy in such form, can’t be transferred

THERMAL EQUILIBRIUM DEFINITION

Thermodynamic equilibrium  is of three types:

1. Mechanical equilibrium. 
2. Chemical equilibrium. 
3. Thermal equilibrium

Thermal equilibrium is when there is no net flow of thermal energy from one system to another and has the same temperature; it also obeys the zeroth law of thermodynamics.

Both thermal and thermodynamic equilibrium are distinct because, in thermodynamic equilibrium, mass and  temperature becomes constant during the operation.

THERMAL EQUILIBRIUM MEANING

Here is the example for thermal equilibrium for a clear understanding. Let us assume two vessels, P and Q, containing gasses.

• PP: the pressure of gasses P
•  VP: Volume of gas P
• PQ: the pressure of gasses Q
•   Vq: volume of gas Q

CASE I – SEPARATED BY ADIABATIC WALL

The wall is coated with insulating material, which doesn’t allow heat to flow through it is called an adiabatic wall. P will be in equilibrium with Q. In this, we cannot say that the two vessels, P and Q, are in equilibrium:

The shaded portion is an adiabatic wall

CASE II – SEPARATED BY DIATHERMIC WALL

The wall that conducts heat flow through it is called a diathermic wall. The flow from one body of higher temperature to another body of lower temperature. The pressure and the volume of P and Q change from (PP, VP) to (P’P, V’P) and (PQ, VQ) to (P’Q, V’Q)  respectively. After the transfer of heat, both the system P and Q will attain equilibrium, so no further flow of heat.

The shaded portion is a diathermic wall.

THERMAL EQUILIBRIUM IN THERMODYNAMICS

If the hot and cold body is placed nearby, the heat in the hot body becomes less, but the heat energy flows from hotter to the colder body. The flow of heat stops when both systems attain equilibrium.

The law of energy conservation in the colder system is defined as the amount of heat loss by the hotter body equal to the amount of heat gained by the colder body:

Q = m×cp×∆T

Where 

• Q- is heat loss or heat gained by the system
• m- the mass of the substance present in the system

For example

A copper ball of mass 5 kg at constant atmospheric pressure and at an initial temperature of 50 degrees celsius is given the heat of 50,000J. Find the change in temperature when the specific heat is 500 J/Kg C

Solution:

Given:- 

m= 5kg

Q = 50,000 J

C = 500 J/Kg C

Q = m×cp×∆T

 ∆T= Temperature

∆T = ∆Q/mcp              

∆T = 50,000/ (5 * 500) 

∆T = 100/5

∆T = 20 C

So the change in temperature is 20 degrees celsius.

MECHANISM INVOLVED IN THERMAL EQUILIBRIUM

• In the system, the temperature is considered the average kinetic energy of the molecular movement
• If two systems of two different temperatures are put together, they are placed side by side. The molecules from the hotter body(fast-moving particles) in one material collide with, the colder body(Slow-moving particles)
• The transfers of heat continue until both systems attain the same temperature. It is based on the second law of thermodynamics as it states the movement of heat from a hotter body to the colder body until it attains the same temperature

For example

• Consider two bodies of different temperatures, say 50 C and 100 C; the heat flows from the body of higher temperature to the body of lower temperature until both bodies attain the same temperature
• Another example of thermal equilibrium is placing the cup of hot tea in the surrounding area. After a while, the cup of tea cools as heat transfers from the cup to the atmosphere, bringing the ambient temperature and the tea temperature to the same level

TWO VARIETIES OF THERMAL EQUILIBRIUM

There are two varieties of thermal equilibrium. They are

1. thermal equilibrium relation between two thermally connected bodies
2. Internal thermal equilibrium of an isolated body

THERMAL EQUILIBRIUM RELATION BETWEEN TWO THERMALLY CONNECTED BODIES

• It refers to the transfer of heat through the selectively permeable partition of matter of work, and it is called a diathermal connection
• According to Lieb and Yngvason, The essential meaning of thermal equilibrium includes spontaneous and balanced, but they have not concluded whether it is finite or non-finite
• After giving a semantic definition, the law of thermodynamics was named, where thermal equilibrium is in a finite relation
• They also established isotherm, which means the same temperature over the period

INTERNAL THERMAL EQUILIBRIUM OF AN ISOLATED BODY

• In this case, thermal equilibrium takes in an isolated body
• The system is completed covered by the black surface, and it does not allow any heat to flow inside or leave outside and allow the temperature to cool down by itself
• When the heat gets cold by itself, the other parameters like temperature, pressure, mass, and some different concentration remains constant then the body is said to have its thermal equilibrium
• A body can attain its internal thermal equilibrium but not its internal chemical equilibrium. For example, glass has an internal thermal equilibrium
• A system won’t directly undergo internal thermal equilibrium; first, it would have gone through fictive thermodynamics operation of partition. It means the transfer of meat between two subsystems (separation by nothing)

DIFFERENCE BETWEEN THERMAL EQUILIBRIUM AND THERMODYNAMICS EQUILIBRIUM

• According to Munster (1970), during thermodynamics, equilibrium does not change the parameters such as temperature, pressure, mass, and other concentration
• Thermal equilibrium is the condition where there is no net flow of thermal energy from one system to another system and has the same temperature; it also obeys the zeroth law of thermodynamics
• In thermal equilibrium, heat flow by direct or indirect contact. There may be no heat flow over a long period which means it stops when both the systems attain the same temperature
• In thermodynamics equilibrium, take when all the other processes and factors remain the same. Heat and all other parameters, such as pressure, mass, and energy, might also transfer in this process

Conclusion

For example, if two gasses, helium, and neon, are trapped in the cylindrical vessels. The gasses get separated by the movable piston(thermal piston). If the pressure inside the helium gas compartment and neon gas compartment remain the same, it means it is thermodynamic equilibrium.