The principle of conservation of heat energy states that

the total amount of heat energy in a closed system remains constant over time. This principle is also known as the first law of thermodynamics. The conservation of heat energy means that energy cannot be created or destroyed, but it can be transferred or transformed from one form to another within the system.

To understand how the principle of conservation of heat energy works, we need to consider the following steps:

1. Identify the system: First, we need to define the boundaries of the system we are analyzing. For example, we can consider an insulated container as our system.

2. Define the variables: Next, we need to define the variables involved, such as the initial and final temperatures, as well as any other relevant properties like mass or specific heat capacity.

3. Calculate the initial energy: Determine the initial amount of heat energy within the system by using the formula: Q = m * c * ΔT, where Q is the heat energy, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.

4. Analyze the energy transfers: Consider any heat transfer mechanisms within the system, such as conduction, convection, or radiation. Identify any heat transfers into or out of the system.

5. Calculate the final energy: Calculate the final amount of heat energy within the system using the same formula mentioned above for all the relevant heat transfers.

6. Compare initial and final energy: Compare the initial and final amounts of heat energy within the system. If they are equal, then the principle of conservation of heat energy is upheld. If they are not equal, it indicates that energy has been gained or lost by the system, violating the principle.

By following these steps, we can analyze the conservation of heat energy within a closed system and determine whether energy is conserved or not.