Understanding the properties of heat is fundamental in physics and thermodynamics. The question asks to identify the statement that is INCORRECT regarding heat. Let's analyze each option carefully to determine its accuracy.

Heat and Temperature Relationship

Let's examine the first statement:

• Statement 1: "The temperature of the two bodies are same even if their heat contents are different."

This statement is CORRECT. Temperature is an intensive property that describes the average kinetic energy of the particles within a substance. Heat content, on the other hand, often refers to the total thermal energy or internal energy of a body, which is an extensive property. An extensive property depends on the amount of matter present. For example, a large bathtub full of water at 25°C has significantly more internal energy (heat content) than a small cup of water at the same 25°C. Both have the same temperature, but their total energy content differs due to their different masses.

Calorimetry and Heat Measurement

Next, let's consider the second statement:

• Statement 2: "It is measured by the principle of calorimetry."

This statement is CORRECT. Heat transfer, or the amount of heat exchanged during a physical or chemical process, is precisely measured using calorimetry. A calorimeter is a device designed to measure the heat flow. The principle of calorimetry states that in an isolated system, the heat lost by a hot body is equal to the heat gained by a cold body until thermal equilibrium is reached.

Heat Content Dependence Factors

Let's evaluate the third statement:

• Statement 3: "Heat content of body depends on its mass, temperature and nature."

This statement is also CORRECT. The amount of heat required to change the temperature of a substance (often related to its heat content or internal energy change) depends on several factors:

• Mass (m): A larger mass requires more heat to change its temperature by the same amount.
• Temperature (\(\Delta T\)): The change in temperature. More heat is needed for a larger temperature change.
• Nature (Specific Heat Capacity, c): Different substances have different specific heat capacities, which is the amount of heat required to raise the temperature of 1 unit mass of the substance by 1 degree. For example, water has a high specific heat capacity, meaning it requires a lot of heat to change its temperature.

This relationship is typically expressed by the formula for heat transfer: \(Q = mc\Delta T\), where \(Q\) is the heat transferred, \(m\) is the mass, \(c\) is the specific heat capacity, and \(\Delta T\) is the change in temperature.

Mixing Bodies and Total Heat

Finally, let's analyze the fourth statement:

• Statement 4: "When two bodies are mixed, total heat is equal to the sum of the heat contents of the two bodies."

This statement is INCORRECT. Here's why:

• Heat vs. Internal Energy: In thermodynamics, "heat" is defined as energy that is transferred between systems (or a system and its surroundings) due to a temperature difference. It is not a property stored within a body. A body possesses *internal energy*, which is the sum of the kinetic and potential energies of its constituent particles. While "heat content" is often used colloquially to mean internal energy, the statement's phrasing is problematic.
• Conservation Principle: When two bodies at different temperatures are mixed in an isolated system, heat flows from the hotter body to the colder body until they reach a common final temperature (thermal equilibrium). The fundamental principle here is the conservation of *energy*. Specifically, the total *internal energy* of the isolated system remains constant before and after mixing. That is, the sum of the initial internal energies of the two bodies equals the final internal energy of the mixture. However, stating "total heat" in this manner is imprecise. The *net heat transfer* within the isolated system is zero (\(Q_{lost} + Q_{gained} = 0\)).
• Heat as a Process Quantity: Heat is a path function, meaning its value depends on the path taken during a process, not just the initial and final states. You cannot simply "sum" heat in the same way you might sum masses or volumes of components to get a total for a mixture because heat itself is energy in transit, not a state function that is simply conserved as a sum of "contents" after interaction. The energy is redistributed, not simply added up as "heat."

Conclusion

Based on the analysis, the statement "When two bodies are mixed, total heat is equal to the sum of the heat contents of the two bodies" is the INCORRECT statement regarding heat, primarily due to the precise thermodynamic definition of heat as energy in transit and the nature of energy conservation in mixing processes.