To understand the differences between internal energy and heat, as well as how these concepts apply when two bodies at different temperatures are mixed in a calorimeter, we need to clarify a few key terms and principles in thermodynamics. Let's break this down step by step.
Defining Internal Energy and Heat
Internal Energy refers to the total energy contained within a system due to the kinetic and potential energies of its molecules. This includes energy from molecular motion (kinetic energy) and energy stored in the bonds between molecules (potential energy). Internal energy is a state function, meaning it depends only on the current state of the system, not on how it got there.
Heat, on the other hand, is the energy transferred between systems (or a system and its surroundings) due to a temperature difference. It is not a property of the system itself but rather a process that occurs when energy is exchanged. When two bodies at different temperatures come into contact, heat flows from the hotter body to the cooler one until thermal equilibrium is reached.
Mixing Two Bodies in a Calorimeter
When two bodies at different temperatures are mixed in a calorimeter, they exchange heat until they reach the same temperature. This process allows us to analyze which quantities remain conserved. Let's evaluate the options provided:
Evaluating the Options
- (a) Sum of temperatures of the 2 bodies: This quantity is not conserved. The temperatures of the two bodies will change as they reach thermal equilibrium, and thus their sum will also change.
- (b) Total heat of the 2 bodies: This is also not conserved. Heat is transferred between the bodies, so the total heat content of the system changes as energy is exchanged.
- (c) Total internal energies of the 2 bodies: This quantity is conserved. The total internal energy of the system remains constant, assuming no heat is lost to the surroundings. The internal energy of each body may change, but the total remains the same due to the conservation of energy principle.
- (d) Internal energy of each body: This is not conserved individually. Each body will experience a change in internal energy as they exchange heat until they reach the same temperature.
Justification for the Correct Answer
The correct answer is (c) total internal energies of the 2 bodies. This is because, in a closed system like a calorimeter, energy cannot be created or destroyed; it can only be transformed from one form to another. When the two bodies exchange heat, the energy lost by the hotter body is equal to the energy gained by the cooler body, thus conserving the total internal energy of the system.
In contrast, the other options fail to hold true because they involve changes in temperature or heat transfer, which are not conserved quantities in this context. The sum of temperatures and total heat are dynamic and change as the system evolves towards equilibrium, while the total internal energy remains constant throughout the process.
Conclusion
In summary, understanding the distinction between internal energy and heat is crucial in thermodynamics. When two bodies at different temperatures are mixed, the total internal energy of the system is conserved, while the individual internal energies and other quantities like temperature and total heat are not. This principle is fundamental in analyzing thermal interactions in calorimetry and other thermodynamic processes.
