The 0th law of thermodynamics states that if two systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium with each other. This law establishes the concept of temperature and allows us to define a common temperature scale.
A real-world example of the 0th law of thermodynamics is the use of a thermometer to measure the temperature of objects. When you bring a thermometer in contact with an object, it allows for the transfer of heat between the object and the thermometer until they reach thermal equilibrium. The thermometer essentially acts as a bridge between the object and a reference system (often a mercury or digital scale) with a known temperature. Once the temperature of the thermometer and the object stabilize, it indicates that they are in thermal equilibrium, and you can read the temperature on the thermometer.
This principle is applied in various everyday scenarios, such as measuring body temperature using a medical thermometer, determining the temperature of liquids or gases in industrial processes, or checking the temperature of food using a cooking thermometer. The 0th law of thermodynamics provides the foundation for these measurements and ensures that consistent temperature scales can be established and used universally.