Prove the total heat gained by an object is equal to the sum of the heat lost by all the surrounding objects – is our subject of discussion today.

**Total heat gained by an object is equal to the sum of the heat lost by all the surrounding objects**

Heat transfer is an important aspect of thermodynamics, which deals with the study of energy and its transformations. Heat can be transferred from one object to another by various modes such as conduction, convection, and radiation. The principle of conservation of energy states that energy cannot be created or destroyed, but it can be transformed from one form to another. This principle is also applicable to heat transfer, which means that the total heat gained by an object must be equal to the sum of the heat lost by all the surrounding objects.

To understand this principle, let us consider an example of two objects A and B in thermal contact with each other. Object A has a temperature T1 and object B has a temperature T2, where T1 > T2. According to the second law of thermodynamics, heat always flows from a hotter object to a cooler object until both objects reach the same temperature.

When the two objects are in thermal contact, heat flows from object A to object B, and as a result, object A loses heat while object B gains heat. Let us assume that object A loses Q1 amount of heat and object B gains Q2 amount of heat. According to the principle of conservation of energy, the total amount of heat lost by object A must be equal to the total amount of heat gained by object B. Mathematically, we can express this as:

Q1 = Q2

This equation represents the principle of the conservation of energy in heat transfer. It states that the total heat gained by an object is equal to the sum of the heat lost by all the surrounding objects.

This principle has practical applications in various fields, such as engineering, physics, and chemistry. For example, in a heat exchanger, the hot fluid loses heat to the cold fluid, and the total heat lost by the hot fluid is equal to the total heat gained by the cold fluid. In a thermodynamic system, the heat gained or lost by the system must be accounted for in the energy balance equation, which is based on the principle of conservation of energy.

In conclusion, the principle of conservation of energy is a fundamental principle of thermodynamics, and it is applicable to heat transfer. The principle states that the total heat gained by an object is equal to the sum of the heat lost by all the surrounding objects. This principle has important practical applications in various fields and is essential for understanding the behavior of thermodynamic systems.

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