Thermal Equilibrium | Physics for EmSAT Achieve PDF Download

Introduction

• Thermal equilibrium arises when two or more objects or thermodynamic systems are connected in a manner that permits the transfer of energy (referred to as thermal contact) but ensures that there is no overall heat energy exchange between them.
• A thermodynamic system represents a defined region of space enclosed by theoretical walls that separate it from the surrounding space. The permeability of these walls to energy or matter depends on the specific type of system.
• In practical terms, thermal equilibrium implies the absence of heat energy transfer between the objects or systems. It can also signify that when one system receives energy from the other, it promptly returns an equal amount of energy, resulting in a net heat transfer of zero.
• Thermal equilibrium finds strong relevance in the field of thermodynamics and its fundamental laws, particularly the zeroth law of thermodynamics.
• The zeroth law of thermodynamics states that if two separate thermodynamic systems are individually in thermal equilibrium with a third system, then they are also in thermal equilibrium with each other.
• Upon reaching thermal equilibrium, both objects or systems share the same temperature, and there is no net flow of heat energy occurring between them.
• Thermal equilibrium can also refer to the uniform distribution of thermal energy within a single object or body. Initially, when thermal energy is applied to a system, it is not evenly spread across the entire object. The point where the thermal energy is applied will have the highest temperature, while other regions within or on the object will exhibit lower temperatures. The initial distribution of heat in the object is influenced by various factors such as material properties, geometry, and the method of heat application. However, as time progresses, the heat energy will gradually disperse throughout the system or object, ultimately achieving internal thermal equilibrium.

Thermal Equilibrium: Temperature

• To comprehend temperature, we must examine the behavior of molecules at the molecular level. Temperature represents a measurement of the average kinetic energy possessed by the molecules within an object. In a given substance, the higher the kinetic energy of the molecules, the hotter the substance becomes. While these molecular motions are commonly visualized as vibrations, it is important to note that vibration is just one aspect. Molecules can also undergo general back-and-forth and left-and-right movements, as well as rotation. The combination of these motions leads to a completely random movement of molecules. Additionally, different molecules exhibit varying rates of motion, and the state of matter (solid, liquid, or gas) also plays a role.
• When a molecule engages in this type of motion, surrounding molecules exhibit similar behavior. Consequently, many molecules interact and collide, bouncing off one another. During these interactions, energy is transferred between molecules, with one gaining energy while the other loses it.

An example of a water molecule engaging in random motion due to kinetic energy.

What Occurs at Thermal Equilibrium?

Now, let's consider the transfer of kinetic energy between two molecules in separate objects, rather than within the same object. The object with a lower temperature will have molecules possessing lower kinetic energy, whereas the object at a higher temperature will exhibit molecules with higher kinetic energy. When these objects are in thermal contact and their molecules can interact, the molecules with lower kinetic energy will gradually absorb more and more energy, subsequently transferring it to the molecules in the object with the lower temperature. This process continues over time until the average kinetic energy of the molecules in both objects becomes equal, resulting in both objects attaining an equal temperature. This state is known as thermal equilibrium, where the objects have achieved a balanced distribution of thermal energy.

Thermal Equilibrium Formula

When it comes to the transfer of heat energy, it's important to not fall into the trap of using temperature when the calculation is involved. Instead, the word energy is more appropriate, and therefore joules is the better unit. To determine the temperature of equilibrium between two objects of varying temperatures (hot and cold), we must first note that this equation is correct:

qhot + qcold = 0

This equation tells us that the heat energy qhot lost by the hotter object is the same magnitude but an opposite sign of the heat energy gained by the colder object qcold, measured in joules. Therefore, adding these two together is equal to 0.

Now, we can calculate the heat energy for both of these in terms of the object properties. To do so, we need this equation:

q = m.c . ΔT

Where m is the mass of the object or substance, measured in kilograms kg, ΔT,  is the temperature change, measured in degrees Celcius ºc (or Kelvin ºk , as their magnitudes are equal) and  is the specific heat capacity of the object, measured in joules per kilogram Celcius

The only thing we have left to determine here is the temperature change ΔT . As we're looking for the temperature at thermal equilibrium, the temperature change can be thought of as the difference between the equilibrium temperature T_e and the current temperatures of each object T_hc and T_cc. With the current temperatures being known, and the equilibrium temperature being the variable that we are solving for, we can assemble this rather large equation:

Where anything underscored with an h regards the hotter object, and anything underscored with a c  regards the colder object. You may notice that we have the variable T_e marked twice in the equation. Once all the other variables are put into the formula, you will be able to combine these into one, to find the final temperature of thermal equilibrium, measured in Celsius.

Example

A block of metal with a mass of 2 kg and a specific heat capacity of 0.5 J/g°C initially has a temperature of 100°C. It is placed in contact with a block of wood with a mass of 1 kg and a specific heat capacity of 1 J/g°C, which initially has a temperature of 20°C. Assuming no heat loss to the surroundings, what will be the equilibrium temperature when thermal equilibrium is reached?

To find the equilibrium temperature, we can use the formula:

(mass1 × specific heat capacity1 × temperature change1) + (mass2 × specific heat capacity2 × temperature change2) = 0
Let's plug in the given values and solve for the equilibrium temperature (Te):
(2 kg × 0.5 J/g°C × (Te - 100°C)) + (1 kg × 1 J/g°C × (Te - 20°C)) = 0
Now, let's simplify the equation:
(1 J/°C × (Te - 100°C)) + (1 J/°C × (Te - 20°C)) = 0
Simplifying further:
Te - 100°C + Te - 20°C = 0
2Te - 120°C = 0
2Te = 120°C
Te = 60°C
Therefore, when thermal equilibrium is reached, the equilibrium temperature will be 60°C.
In this example, the metal block and the wood block initially have different temperatures, and through the process of thermal contact and energy transfer, they reach a state of thermal equilibrium where their temperatures equalize.