The Zeroth Law of Thermodynamics states that if two bodies are each in thermal equilibrium with a third body, then they are also in thermal equilibrium with each other. Thermal equilibrium means that when two systems are connected by a barrier that allows only heat transfer, there is no net heat flow between them because their temperatures are equal. This law forms the basis for the concept and measurement of temperature. It can be explained using three systems. A, B, and C. Systems A and B are separated by an insulating (adiabatic) wall, and system C is connected to both by a conducting (diathermic) wall, as shown in the figure.
Since energy can be exchanged between systems A and C, both are in thermal equilibrium. Similarly, energy can be exchanged between systems B and C, so B and C are also in thermal equilibrium. In other words, systems A and B are separately in thermal equilibrium with the third system C.
When the adiabatic wall between A and B is removed, no energy transfer takes place between them. This shows that systems A and B are also in thermal equilibrium with each other.
This observation leads to an important law called the Zeroth Law of Thermodynamics, which states that if two bodies are in thermal equilibrium with a third body, then they are also in thermal equilibrium with each other.
According to Zeroth’s Law of Thermodynamics, if system A is in thermal equilibrium with system C, then
Temperature of System A = Temperature of System C
Similarly, if system B is in thermal equilibrium with system C, then
Temperature of System B =Temperature of System C
Now, from the above relation, we have
Temperature of System A = Temperature of System B
Thermal Equilibrium
The Zeroth Law of Thermodynamics recognizes temperature as an important physical quantity because it helps predict whether heat will flow between objects. This is true regardless of how the objects interact. Heat can transfer between two bodies even without direct contact, such as through radiation, which is one of the methods of heat transfer.
According to the Zeroth Law of Thermodynamics, when systems are in thermal equilibrium, no heat flow occurs between them. Temperature is therefore a key concept in thermodynamics, as it helps distinguish between hot and cold bodies. When two or more bodies at different temperatures come into contact, heat flows from the hotter body to the colder one until they reach the same temperature, and this state is known as thermal equilibrium.
Zeroth Law of Thermodynamics Example
The zeroth law of thermodynamics states that heat energy flows between two bodies when they are kept in contact with each other.
For example, if we take three bodies, P, Q, and R, at different temperatures that are in contact with each other, then the heat transfers among the three bodies till they reach thermal equilibrium; in this case, they reach a constant temperature.
Thermal equilibrium can also be achieved even when the temperatures of the bodies are different.
For example, if we take two bodies, A and B, and contain them in adiabatic chambers (which do not allow heat to pass through them), then if they are allowed to be in contact still, there is no heat transfer, as adiabatic chambers do not allow heat to pass through them, so they are considered to be in thermal equilibrium.
The zeroth law of thermodynamics follows the translation relation between various bodies, i.e., if we take three bodies A, B, and C, then if A and B are in thermal equilibrium and B and C are in thermal equilibrium, then A and C are also considered to be in thermal equilibrium.
Application of Zeroth Law of Thermodynamics
- The law is fundamental for the mathematical formulation of thermodynamics and defining temperature.
- It is used to compare temperatures of different systems.
- Accurate temperature measurement requires a reference body and a property that changes with temperature, known as a thermodynamic property.
- Thermometers are the most common application of the Zeroth Law.
- In a mercury thermometer, as the temperature rises, the mercury expands, increasing its height in the tube. This change indicates temperature, demonstrating the law in action.
Depending on their thermometric characteristic, several types of thermometers can be utilized. The following is a list of thermometers.
- Constant pressure gas thermometer - Volume
- Constant volume gas thermometer - Pressure
- Electrical resistance thermometer - Resistance
- Mercury-in-glass thermometer - Length
- Thermocouple - Thermal e.m.f.
When you have two glasses of water, you have another illustration of the zeroth law of thermodynamics. One glass will be filled with hot water, while the other will be filled with cold water. If we leave them on the table for a few hours, they will achieve thermal equilibrium with the room's temperature.
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Solved Problems
Question 1: Two equal masses of water are in separate containers. One is at 80°C and the other at 40°C. They are mixed in an insulated container. What will be the final temperature of the mixture?
Solution: the masses are equal, and no heat is lost
T_\text{final} = \frac{T_1 + T_2}{2}
= \frac{80 + 40}{2}
= 60^\circ\text{C}
Question 2: A copper rod at 90°C is brought in contact with an aluminum rod at 30°C. If no heat is lost to the surroundings, which rod gains heat and which loses heat?
Solution:
- Copper rod (
90^\circ\text{C} ) is hotter → loses heat- Aluminum rod (
30^\circ\text{C} ) is colder → gains heatAt thermal equilibrium, both rods reach the same temperature.
Q lost by copper = Q gained by aluminium
Question 3: A mercury thermometer shows 25°C initially. It is placed in a liquid, and after some time, the mercury rises to 55°C. What is the temperature of the liquid?
Solution: When the thermometer is placed in the liquid, heat flows between the mercury and the liquid until they reach thermal equilibrium. According to the Zeroth Law of Thermodynamics, two systems in thermal equilibrium have the same temperature. Therefore, when the mercury stops rising, it shows that the thermometer and the liquid are at the same temperature, which is 55°C.