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In my textbook, it says that when gas molecules have no kinetic energy, they also have no thermal energy. However, the textbook defines thermal energy as the sum of the kinetic and potential energies of all atoms in a system. What I'm thinking is that since the molecules have no kinetic energy, then the atoms have no kinetic energy, which means that all their energy is now potential energy. Thus, the gas molecules would have thermal energy. How am I wrong?

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First of all, the state of affairs of having a collection of atoms or molecules that all have zero kinetic energy is called absolute zero.

One of the flaws in your wording is when you say:

What I'm thinking is that since the molecules have no kinetic energy, then the atoms have no kinetic energy, which means that all their energy is now potential energy.

The part of this that is flawed is the part about thinking that "all of their energy is now potential energy". Based on what you have written, it seems as if you believe that a decrease in temperature means atoms or molecules have converted kinetic energy into potential energy. This isn't correct. Cooling off involves an overall decrease in atoms' kinetic energy because that energy has been pulled out of the contained altogether, somehow.

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Kinetic energy is energy of motion. Potential energy is energy of position or configuration. Heat absorbed or released may of course change the kinetic energy and thus temperature of a substance. But heat can also be absorbed or released with no change in temperature (kinetic energy) such as with the latent heats which cause phase changes. The energy absorbed or released in phase changes is associated with the potential energy stored in the bonds between particles. So we do have an association between thermal energy and both kinetic and potential energy. But temperature is only associated with kinetic energy. Hope this helps.

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when gas molecules have no kinetic energy, they also have no thermal energy. However, the textbook defines thermal energy as the sum of the kinetic and potential energies of all atoms in a system.

Let us examine your statement on the basis of "kinetic Theory of gas molecules"

We use the kinetic theory of gases to see a collection of gas molecules in a container.

The Theory relate the temperature, pressure, and volume of a gas back to what the individual molecules in the gas are doing.

The temperature of a substance is a measure of how fast its molecules are moving—or in other words, a measure of the average kinetic energy of the molecules.

No Kinetic Energy to individual molecules means a state of the system which have been driven to a point which is unrealistic/hypothetical.

The kinetic theory of gases lets us relate the kinetic energy of the molecules in a gas to the temperature, volume, and pressure of the gas.

The theory makes several assumptions:

The gas is made up of a very large number of identical molecules, N and

are moving randomly in all possible directions.They only interact with

each other and the walls of the container, **scattering around in many

zillions** of tiny, adorable collisions which are elastic.

What that last one means is that no energy is lost in the form of heat when

the two objects collide. Therefore, after each collision the molecules still have the same kinetic energy.

This is important, because if collisions caused molecules to lose kinetic energy, after thousands and billions of collisions, the molecules would have no kinetic energy (speed) at all.

This would cause gases to cool into liquids which in turn would cool and solidify over time just because the molecules in them are losing energy in their collisions.

Eventually, the universe would consist of one solitary solid mass at absolute zero.

Hope you like your neighbors, because you're stuck with them in the frozen universe ball for the rest of eternity. At least, that's what would happen, if we weren't making that last assumption.

Therefore, I think one should not go to a zero kinetic energy state and try to look at the potential energy and events on the basis of our model.

Even the ground state energy of oscillators do not move to zero as their exists residual motions.

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