Question:

Is it possible for the work done during a process at constant pressure and volume to be fully transformed into thermal energy?

Answer:

states that the total energy of an isolated system is constant. Energy can be transferred from one form to another, but it cannot be created or destroyed. This law is often expressed as: $$\Delta U = Q – W$$

where \(\Delta U\) is the change in internal energy of the system, \(Q\) is the heat added to the system, and \(W\) is the work done by the system.

When a process occurs at constant volume, no work is done by the system since work (\(W\)) is defined as:

$$W = P \Delta V$$

where \(P\) is the pressure and \(\Delta V\) is the change in volume. At constant volume (\(\Delta V = 0\)), the work done is zero. Therefore, any heat (\(Q\)) added to the system at constant volume goes entirely into changing the internal energy (\(\Delta U\)).

However, when a process occurs at constant pressure, the work done is not zero, as the system may expand or contract, and thus, work is involved. In such a scenario, not all the work can be converted into thermal energy because some of the energy is utilized in doing work against the external pressure.

In conclusion, at constant volume, it is indeed possible for all the work to be transformed into thermal energy, as there is no work done on or by the system. At constant pressure, however, only a portion of the work can be converted into thermal energy, with the rest being used to do work against the external environment. This distinction is crucial for understanding various thermodynamic processes and designing systems like engines and refrigerators, where the interplay between heat and work is fundamental to their operation.