Given that the equation for the first law of thermodynamics:

$$Q - W = \Delta E$$

It is known that $\Delta E$ is equal to the change in internal energy, kinetic energy, and potential energy. and that $Q$ is the total heat transfer and $W$ is the work transfer.

I'm kind off confused when analyzing systems using the said equation. So here are some questions I had in mind.

  1. It was discussed to me that when analyzing a closed system $\Delta E$ is always zero since there would be no change in the total energy of the system. Is this always true?

  2. In analyzing open steady systems, it is said that the change in kinetic energy and potential energy is always zero but the change in internal energy may not be zero in certain situations. That said, when will we know when the change in internal energy changes? Is it changed when the system changes pressure or volume or temperature?

  3. There is also another form of Total energy in the system called mechanical energy, When will we know what to use in analyzing systems? Is it the formula for mechanical energy or the formula for energy in terms of internal, potential, and kinetic energy?

  4. Also, there is also an alternative equation considering the flow rates of the system. When will we know when to use the regular equation and the one using the flow rates?


This is not a systematic set of answers to your questions, but a few observations that might help…

  1. A closed system is usually taken to mean a system in which the number of particles is fixed. There is no ban on heat entering or leaving or work being done on or by the system, so $\Delta E$ is not always zero.

  2. The kinetic energy that contributes to the internal energy of the system is that of particles in the system, as reckoned in the frame of reference of the centre of mass of the system. So if the system (e.g. a cylinder of gas) is hurled through the air at high speed, this won't increase its internal energy.

  3. 'Mechanical energy' is not, as far as I know, a term with a meaning in thermodynamics, as understood by physicists.

  4. For a given sample of a fluid, it's possible to express internal energy as a function of two variables, for example volume and temperature. The simplest example is an ideal gas, for N molecules of which the internal energy is given by $$U=\frac{3}{2} NkT$$ in which T is the kelvin temperature.


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