17. Conservation of energy law in heat processes
First Law of Thermodynamics

In the second book the law of energy conservation in mechanics was studied in detail. It has been shown that if between bodies are acting forces that depend only on distance, then the transition of the body system from the initial state of 1 to the final state of 2, the change in energy is equal to the work of external forces

\( E_2 - E_1 = \Delta W \) (1-20)

After we have found out that along with mechanical energy of a body possess also internal energy which can change not only at work performance, but also at heat transfer, the law of conservation of energy (1-20) can be summarized on heat processes.

The change of total system energy (mechanical E and internal U) from initial state 1 to final state 2 is equal to the work of external forces plus the quantity of heat transferred to the system

\( (E_2 + U_2) - (E_1 + U_1) = \Delta W + \Delta Q \)

The theory of heat phenomena usually considers bodies whose center of gravity does not change much. In this case, the mechanical energy of bodies practically does not change \( E_2 = E_1 \).

Considering mechanical energy of a body unchanged, it is possible to formulate the law of conservation of energy as follows. Change of internal energy at transition of a body from one condition to another is equal to work of external forces plus quantity of the transferred heat

\( \Delta U = \Delta W + \Delta Q \) (1-21)

This is the first law of thermodynamics. In the particular case where a given body is thermally isolated from surrounding bodies \( \Delta Q = 0 \), the change in internal energy can only be done by work \( \Delta U = \Delta W \).

The processes happening in a heat-isolated system are called adiabatic.

It should be emphasized that if in mechanics the law of energy conservation is a consequence of the laws of mechanics, the general law of energy conservation is the result of summarizing experimental facts. This is an experimental (empirical) law.

The first law of thermodynamics allows to determine the change of internal energy at the transition of the system from the initial state to the final one. The internal energy itself is determined with precision to an arbitrary constant, because when \( U_1 \) and \( U_2 \) are changed by the same value, the difference of \( U_1 - U_2 \) remains the same.

In a closed system, a system that is not impacted by external forces \( \Delta W = 0 \) and heat is not transferred there \( \Delta Q = 0 \), the energy remains unchanged \( \Delta U = 0 \).

It is important to realize that the work and the quantity of heat transferred to the system determine the change in the energy of the system, but they are not identical to the energy. They characterize not the system state itself, as the internal energy, but determine the process of energy transfer at the state change. It is impossible to say that the system contains a certain quantity of heat or work. Only internal energy has a certain value for the system. The system can reduce the internal energy reserve by giving off heat without performing work or, conversely, by performing work without giving off heat.

For example, the heated gas in the cylinder can cool down without performing any work, giving heat to the surrounding bodies. But the gas can lose the same quantity of internal energy by moving the piston without giving heat to the surrounding bodies. To do so, the cylinder walls and piston must be thermally impermeable.

On the other hand, if the change of internal energy always means the change of the state of the system, then the change of the state does not necessarily correspond to the change of internal energy: the same internal energy may correspond to different states.

So, when you put a heated piece of iron in the calorimeter, the condition of the system water - iron will change: water will heat up, iron will cool down. However, the internal energy of the whole system will not change, as the system is isolated and external forces do not work on it.