# Kinetic energy of molecule depends upon?

1. Jul 3, 2014

### Hardik Batra

Average kinetic energy of a molecule is = (3/2)kT

Avg. K.E is directly proportional to temp.(T) only.

As you increase temp of gas then K.E will also increase.

In my book given that,

Average K.E is independent of pressure, Volume or nature of the gas.

When you increase the pressure of a gas temp of gas will increase (gay lussac's law )
if temp. increase then Avg. K.E of gas also increase.

Then how the K.E is independent from pressure.

2. Jul 3, 2014

### Matterwave

For an ideal gas, the average K.E. is dependent only on temperature. It's dependence on pressure or other state variables is only manifest through a temperature change. If you had an isothermal change in pressure (and therefore volume), the average kinetic energy would not change.

3. Jul 3, 2014

### Hardik Batra

This is true for isothermal process.
But if you increase the pressure of gas rapidly. Then temp. of gas will increase. And K.E is depends upon pressure.

4. Jul 3, 2014

### Matterwave

Yes, but in such a case, you can still express the energy as 3/2kT. Maybe it helps if I tell you that you can use the ideal gas law to re-express the energy as 3/2(PV/N)=3/2(P/n).

It is usually more convenient to look at things from the temperature perspective.

What the book means when it says "only dependent on temperature" is that if the process is isothermal, the energy won't change. If the process is not isothermal, then the energy change can be found as a function of the temperature change. What more could you want?

5. Jul 3, 2014

### 256bits

In that case, two variables are changing, so which one is it? temperature or pressure. Actually you can add in another - volume if the mass of the gas in question does not change. Or if you want to keep the volume constant, then the amount of gas has to change. The question one has to ask is, by keeping certain variables constant which one has an affect on the KE.

Keeping temperature constant, and changing pressure does not affect the kinetic energy.
Keeping temperature constant and changing volume does not affect kinetic energy.

6. Jul 3, 2014

### Simon Bridge

This is not correct - that formula applies only to a mono-atomic ideal gas. Not a molecular gas.
Not a gas made of components which have an internal structure.

It only applies to that randomized kinetic energy which manifests as temperature.
For instance, if I take a bottle of gas, put it in the trunk of my car and drive off, all the gas particles gain kinetic energy from that which does not (mostly) end up as temperature. It is still kinetic energy.

So it should not be surprising to find out that the energy that manifests as temperature:
... you basically have it backwards: temperature is a manifestation of the random particle kinetic energy - thus temperature depends on kinetic energy, not the other way around.

The equation does not say that the average KE does not change if pressure or volume changes. It only says that this is how you get the average KE by working backwards from the known temperature. Anything that changes the temperature means that the average kinetic energy per molecule has changed. This is what being dependent only on temperature means.

The ideal gas equation of state is PV=nRT ... so you see that temperature is related to the other state variables too. Writing KE=3kT/2 is also saying that KE=3kPV/2nR.

You may benefit from a more formal review of classical thermodynamics:
http://home.comcast.net/~szemengtan/StatisticalMechanics/ClassicalThermodynamicsReview.pdf [Broken]
From this, we see that the internal energy of a ﬁxed mass of ideal gas (so that N is ﬁxed) depends only on the temperature and not the volume or pressure. The fact that the internal energy of an ideal gas depends only on the temperature is known as Joule's law, and is a consequence of the assumption that the particles do not interact. Jouleís law is true for all ideal gases, but the coeﬃcient 3/2 [the] equation ... holds only for a monatomic gas.
-- p1.6 following eq(1.5)​

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