What is Thermal Equilibrium

We all feel the heat when we are exposed to fire or we step outside in the sun or whenever we take a sip from a hot cup of coffee. Similarly, we feel a chill while drinking a can of soda or Coke or if we step into the bathtub or go out at night. Have you ever thought about why this happens? What exactly is hot and cold? How are they related to temperature? What effects do our bodies undergo whenever we touch a hot or cold substance? Well, we are going to discuss all of this here under a heading called thermal equilibrium. In simple words, thermal equilibrium provides a framework to establish a connection between heat and temperature. So without further ado, let’s dive in! 

What is Thermal Equilibrium? 

Two physical bodies are said to be in thermal equilibrium if there is no net transfer of heat if they are connected by the path which allows heat transfer. Thermal equilibrium follows the Zeroth Law of Thermodynamics. In the case of thermal equilibrium, both the bodies in consideration have the same temperature. Suppose, you put a mug of hot water into a freezer. The hot water will cool down with time. We all know that. Now the question that arises here is why the temperature of the hot water cools down until it attains the temperature of the freezer. This phenomenon is an example of nothing but thermal equilibrium. 

Thermal Equilibrium Definition

Thermal equilibrium is the physical state of two bodies when they are connected by a permeable path, don’t undergo any heat transfer and both the bodies have the same temperature. 

In simple words, the temperature is the measure of the average kinetic energy of the molecules in an object. When two objects come in contact with each other, the faster-moving molecules from one object with higher temperature collide with the slower-moving molecules in the object with lower temperature, the transfer of heat energy occurs and the temperature of the two bodies gradually becomes the same. 

Thermal Equilibrium and Thermodynamic Equilibrium

A system is said to be in thermodynamic equilibrium if there is no macroscopic change such as a change in entropy, internal energy and other. The thermodynamic equilibrium of a body is determined by its intensive properties like temperature, pressure, volume, mass etc. Thermodynamic equilibrium is similar to the inertia of a body i.e. a body in thermodynamic equilibrium tends to remain in its state and don’t change spontaneously. For a body to be in thermodynamic equilibrium, it must satisfy three conditions: 

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

A body to be in thermal equilibrium must have the same temperature throughout and there should not be any heat exchange going on with the object and its surroundings. Again, a body in thermodynamic equilibrium must be in thermal equilibrium but vice versa is not always true. 

Thermal Equilibrium Equation

The thermal equilibrium of two bodies in contact can be obtained by the formula:

                                                       Q = m.c.ΔT

where 

Q is the total energy in joules

m signifies the mass of the objects

c is the specific heat of a substance in joules per kilogram per kelvin i.e. {J/kg.K}

Specific heat: It is the amount of heat energy required to raise the temperature of one unit mass of any substance by one degree. It is expressed in units as joules per kilogram per kelvin. Specific heat capacity is an intrinsic quality of a substance i.e. it is independent of the shape or size or amount of the substance that is being considered. 

Sample question related to Thermal Equilibrium

What will be the equilibrium temperature of the mixture if 20 grams of water at  5 degrees celsius is mixed with 100 grams of water at an initial temperature of 60 degrees celsius? 

Solution:

Mass of cold water: 0.02 kg

Mass of hot water: 0.1 kg

Specific heat constant of water: 4190 J/kg⋅K

As per the equation of thermal equilibrium:

Q = m.c.(Final temperature – Initial temperature)

Q = m.c.ΔT

Final temperature =

 Initial temperature=

Here the system goes into equilibrium, then heat exchange with the surrounding is zero i.e. 

Now,                 Heat exchange by cold body or fluid + Heat exchange by hot body or fluid  =0

                                               So, Final temperature = 50.83 degree celsius.

Thermal Equilibrium of Earth

For the survivability of humans and other lifeforms, Earth must maintain its thermal equilibrium i.e. the temperature remains constant throughout. The heat energy that the sun radiates in the earth’s atmosphere must be balanced to maintain the temperature of the planet i.e. net incoming heat should be equal to net heat energy leaving the earth’s atmosphere. However, this is an ideal condition and doesn’t happen often. 

With the increasing effect of greenhouse gases and environmental degradation, the ability of Earth’s atmosphere to transfer heat back to space has slowed down, making the planet hotter. Although greenhouse gases are important for the survival of humans, it helps in maintaining the habitable temperature of the planet and keeps it from going too cold to live. But at the same time, the increasing discharge of carbon dioxide, Methane and Nitrogen dioxide has hampered the energy flow of the Earth’s atmosphere. This change in the amount of heat flow in and out of the Earth’s atmosphere has resulted in global warming, environmental crisis, melting of the icebergs, increasing sea levels and so on. 

Conclusion

As mentioned above, A body to be in thermal equilibrium must have the same temperature throughout and there should not be any heat exchange going on with the object and its surroundings.Thermal equilibrium is a crucial aspect for the survival of life on Earth. The body in thermal equilibrium is reflexive and symmetric. However, it is not transitive. Thermal equilibrium laid the groundwork for the “Zeroth Law of Thermodynamics”. Such bodies in the thermal equilibrium are known as isotherms.