What is the zeroth law of thermodynamics ? What does the transitive property of temperature mean ?
The Zeroth Law of Thermodynamics states that if two systems are in thermal equilibrium with a third system, they are also in thermal equilibrium with each other. In simpler terms, if system A is in thermal equilibrium with system B, and system B is in thermal equilibrium with system C, then system A is also in thermal equilibrium with system C. This law lays the foundation for the concept of temperature and allows for the establishment of a temperature scale.

The transitive property of temperature is a direct consequence of the Zeroth Law of Thermodynamics. It means that temperature has a transitive relationship among systems. If the temperature of system A is equal to the temperature of system B, and the temperature of system B is equal to the temperature of system C, then the temperature of system A is also equal to the temperature of system C. This transitive property allows us to compare the temperatures of different systems and determine whether they are in thermal equilibrium with each other.
Is there a reason why it is called the Zeroth law and not included in the three Laws of Thermodynamics? How is the Zeroth Law related to the other three Laws of Thermodynamics?
The reason it is called the Zeroth law of thermodynamics is that it was added later to the original three laws, which were first formulated by German physicist Rudolf Clausius in the mid-19th century. The term zeroth was used to emphasize the importance of this law as a fundamental and necessary prerequisite for the other three laws.

The Zeroth Law of Thermodynamics is related to the other three laws in that it provides the basic definition and framework for the concept of temperature, which is essential for understanding and applying the other three laws. The first law of thermodynamics, also known as the law of energy conservation, states that energy can neither be created nor destroyed, but can be converted from one form to another. The second law of thermodynamics, also known as the law of entropy, states that the total entropy of a closed system will always tend to increase over time. The third law of thermodynamics states that as the temperature of a system approaches absolute zero, the entropy of the system approaches a minimum value.

Without the Zeroth Law of Thermodynamics, the other three laws would not be possible to state or apply, as the concept of temperature would be undefined. The Zeroth Law provides a foundation for the other laws by establishing a consistent and objective way of measuring and comparing the temperatures of different systems.