If the external world does work on the system, the energy of the system increases , decreases or remains the same? I think it increases. Am I correct?
The system increases. Yes, you are correct.
Actually, you are incorrect. When the external world does work on a system, the energy of the system increases.
To understand why this is the case, let's first define work and energy. Work is defined as the transfer of energy from one object to another. Energy, on the other hand, is the ability of a system to do work.
Now, when the external world does work on a system, it is transferring energy to the system. This means that the system is gaining energy, which results in an increase in its energy.
To illustrate this, consider the example of a person pushing a box across a floor. The person exerts force on the box, which results in work being done. This work is transferred to the box, increasing its energy. As a result, the kinetic energy of the box increases as it starts to move.
Therefore, when the external world does work on a system, the energy of the system increases.