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Leoragon
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I'm confused with this topic. However, I think I know a bit. There's something to do with the temperature and it affects the energy of the molecules.
Can someone help?
Can someone help?
AbsoluteZer0 said:Temperature is the average kinetic energy of the molecules of a substance.
Rap said:Another nit-pick - the zeroth law holds for any system, not just a gas.
the_emi_guy said:I don't see where AbsoluteZer0 implied that the zeroth law only applied to a gas.
the_emi_guy said:Nice summary, but here is a nit-pick:
Temperature is *proportional* to average kinetic energy. Specifically for monatomic gases:
[tex] \bar {E} = \frac{3}{2}k_bT [/tex]
the_emi_guy said:Temperature is directly proportional to average kinetic energy of molecules.
In other words if I double the temperature (kelvin scale), then I have also doubled the average kinetic energy of the molecules.
The constant of proportionality depends on the particular substance, but there is a whole class of substances called monatomic gasses that have the same constant.
[tex] \bar {E} [/tex]
Average kinetic energy of molecules.
[tex] k_b[/tex]
Boltzmann constant
[tex] T [/tex]
Temperature
It's the energy per state rather than the energy per molecule. Diatomic gases have more states than monatomic ones in which to store energy, so pack more energy per molecule for the same temperature.the_emi_guy said:Temperature is directly proportional to average kinetic energy of molecules.
haruspex said:It's the energy per state rather than the energy per molecule. Diatomic gases have more states than monatomic ones in which to store energy, so pack more energy per molecule for the same temperature.
Kinetic energy includes center of mass motion only. So it doesn't matter how many other degrees of freedom the molecule has. The average kinetic energy will always be 3/2 kbT.the_emi_guy said:Nice summary, but here is a nit-pick:
Temperature is *proportional* to average kinetic energy. Specifically for monatomic gases:
[tex] \bar {E} = \frac{3}{2}k_bT [/tex]
K^2 said:Kinetic energy includes center of mass motion only. So it doesn't matter how many other degrees of freedom the molecule has. The average kinetic energy will always be 3/2 kbT.
The total internal energy will scale differently depending on molecular structure, and that has to be taken into account if you are considering heat capacities. But if you are interested in kinetic energy of molecules only, then you don't have to worry about any of it.
K^2 said:Kinetic energy includes center of mass motion only. So it doesn't matter how many other degrees of freedom the molecule has. The average kinetic energy will always be 3/2 kbT.
The total internal energy will scale differently depending on molecular structure, and that has to be taken into account if you are considering heat capacities. But if you are interested in kinetic energy of molecules only, then you don't have to worry about any of it.
Vibrational DoF includes kinetic and potential contributions. That's where the double-count of these DoF comes from. Rotational is purely kinetic, yes, but usually when people talk about "average kinetic energy," they are referring to translational part only. Otherwise, it becomes unclear what you mean. Including kinetic term, but not potential term from vibrations would be just silly, for example. And looking at just translational and rotational doesn't make much sense either.the_emi_guy said:Perhaps this is just semantics, but I was taught that all of the thermal energy was kinetic. The motion of the center of mass being the translational kinetic energy, plus the internal kinetic energy in the form of lattice vibrations/rotations etc. Quantum mechanics was required in order to get the right count of degrees of freedom, but that it was all kinetic energy.
If you talk only about translational kinetic energy, which is what is usually meant by "average kinetic energy", then it's always 3/2.Leoragon said:So, in a nut shell, temperature is proportional to the kinetic energy? And there's that formula that shows the average kinetic energy of a monoatomic gas. For diatomic, its 5/2?
If you talk only about translational kinetic energy, which is what is usually meant by "average kinetic energy", then it's always 3/2.
If you look at total mechanical energy of a diatomic gas, you get 3/2 from translational DoF, 2/2 from rotational, and 2/2 from vibrational, of which 6/2 total is kinetic and 1/2 is potential energy. However, some of these will be "frozen out". Specifically, rotational degrees of freedom are usually inaccessible because the quantum of energy is much higher than available amount of energy at room temperatures. So you end up with roughly 5/2 total mechanical energy for diatomic gases.
With triatomic it depends on whether all three are different, and if not, how they are arranged. For CO2, H2O, and similarly structured molecules, you get something very close to 7/2, because rotational modes are still frozen out, but you pick up an extra vibrational mode.Leoragon said:What? So average kinetic energy is 3/2, and the total mechanical energy is 5/2? What happens when the molecule is triatomic? Is it the same?
Kinetic energy is the energy that an object possesses due to its motion. It is a form of energy that is associated with the movement of molecules, atoms, or particles.
The average kinetic energy of molecules is calculated by taking the sum of the kinetic energies of all the molecules in a system and dividing it by the total number of molecules. This gives us the average kinetic energy per molecule in the system.
The average kinetic energy of molecules can be affected by temperature, mass, and velocity of the molecules. As temperature increases, the average kinetic energy of molecules also increases. Similarly, as mass and velocity increase, the average kinetic energy of molecules also increases.
The average kinetic energy of molecules is directly proportional to the temperature of the system. This means that as the temperature of a system increases, the average kinetic energy of molecules also increases. This relationship is described by the kinetic theory of gases.
Understanding the average kinetic energy of molecules is important in various fields of science, such as thermodynamics, chemistry, and physics. It helps us understand the behavior of gases, the properties of matter, and the principles of energy transfer. It also has practical applications in industries such as energy production and transportation.