Question

The law on principle of method of mixtures is based on

Answer 1

We know that two or more materials at various temperatures are placed together within a calorimeter. The materials will share thermal energy until the thermal equilibrium is established. At thermal equilibrium, all the materials reach the same temperature.

Complete answer:
The principle of the method of mixtures tells us that the heat lost by a hot body is equal to the heat gained by the cold body when they are mixed together and attain the equilibrium condition or the same temperature. This principle is based on the law of conservation of energy. A Heat lost by the hot body is equal to the Heat gained by the cold body.
The calorimeter is a device used to measure the heat flow of a chemical or physical reaction. Calorimetry is the process of measuring this heat. It consists of a metal container to place water above the combustion chamber and a thermometer to measure the temperature change. The principle of calorimetry is if two bodies at two different temperatures are brought into thermal contact, then heat is lost by the hot body, and heat is gained by the cold body until they attain thermal equilibrium.
This is known as the principle of the method of mixture. It is based on Newton’s Law of Cooling, which states that the rate of loss of heat energy of a hot body is directly proportional to the temperature difference between the body and its surrounding provided the temperature difference should be small. This law is also called the principle of calorimetry. This principle is based on the law of conservation of energy.
When a hot body is mixed (or kept in contact) with a cold body, heat energy passes from the hot body to the cold body, till both the bodies attain the same temperature, if no energy is lost to the surroundings, i.e., if the system is fully insulated. Heat lost by the hot body = Heat gained by the cold body.

Note:
Remember that Calorimetric is a branch of science which deals with the measurement of heat. The Calorimeter is the apparatus used for this purpose. A perfect calorimeter completely prevents heat flow into or out of the system contained within it.