Internal energy does or does not depend on volume of molecules?

[p3t3r1]

I am kind of confused by the conflict of the following two concepts.

If I understood correctly, internal energy of a system is independent of the volume occupied by the gas molecules. This is because the gas molecules are assumed to be ideal and therefore have no intermolecular interactions. (Hence volume doesn't matter)

This is proven to be true in adibatic change, where both volume and temperature changes.

If I understood correctly, this adibatic change can be divided into volume change at constant temperature, and temperature change at constant volume.

However, for the change in the internal energy, only the second step matters and hence delta U = Cv (Tf-Ti)

I fail to see how this applies in expansion work. In expansion work, delta U = w + q.

w = Pex x delta V for irreversible expansion

and

w = -nRTln(Vf/Vi) for isothermal reversible expansion.


Well if work is done, then the internal energy must change. So wouldn't this mean that the internal energy is dependent on the volume of the molecules?

(Unless of course the heat supplied by the surroundings is equal to the work done by the system to keep the process isotherma; and these two cancel each other out to give delta U = 0?)

Thanks!

 

[atyy]

(Unless of course the heat supplied by the surroundings is equal to the work done by the system to keep the process isotherma; and these two cancel each other out to give delta U = 0?)

Yes:
http://hyperphysics.phy-astr.gsu.edu/Hbase/thermo/isoth.html

 

[sir-pinski]

The concept of internal energy is a bit complex and can be confusing, so let's break it down. Internal energy is the total energy of a system due to the motion and interactions of its particles. It includes kinetic energy, potential energy, and any other forms of energy that may be present in the system.

In an ideal gas, the molecules are assumed to have no intermolecular interactions, meaning they do not attract or repel each other. This means that the internal energy of an ideal gas is solely dependent on the temperature of the system, as temperature is a measure of the average kinetic energy of the molecules. In this case, the volume of the molecules does not affect the internal energy because there are no interactions between the molecules.

In an adiabatic change, where both volume and temperature change, the internal energy is still independent of the volume of the molecules. This is because the change in internal energy is only due to the change in temperature, not the change in volume. As you mentioned, in an adiabatic change, the change in internal energy can be divided into two steps: a volume change at constant temperature and a temperature change at constant volume. However, only the temperature change at constant volume affects the internal energy, as the volume change does not involve any energy transfer.

In expansion work, the internal energy does change because work is being done by or on the system. In an irreversible expansion, the work done is equal to the external pressure (Pex) multiplied by the change in volume (delta V). In this case, the internal energy of the system decreases because the system is doing work on the surroundings. In an isothermal reversible expansion, the work done is equal to -nRTln(Vf/Vi), where n is the number of moles, R is the gas constant, and T is the temperature. In this case, the internal energy does not change because the heat supplied by the surroundings is equal to the work done by the system, resulting in a net change of zero.

So, to answer your question, the internal energy of a system does not depend on the volume of the molecules. It is only affected by the temperature and any work or heat transfer that occurs. I hope this helps clarify any confusion.