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In a close system, when no.of mole of gas molecules increase, gas expansion happens, and its plug is being pushed outward.

What i want to ask is that: Where does the energy comes from which does work on the plug?Does the energy come from the vibrational energy or translation energy of the molecules?

Another question is that if no gas expansion is allowed in that system,what conclusion can I make by equation PV=nRT?Will the temperature,or the air pressure inside that system keep constant ?

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In a close system, when no.of mole of gas molecules increase, gas expansion happens, and its plug is being pushed outward.

What i want to ask is that: Where does the energy comes from which does work on the plug?Does the energy come from the vibrational energy or translation energy of the molecules?

Energy put into a system will in some sense spread evenly over all possible energy contributions. I.e. whatever form of energy you give your new particles, after a while all particles will have certain average translational energies and certain average vibrational energies (assuming your gas particles can vibrate, of course). What actually pushes of course is the motion of the particles, not their rotation or vibration.

Another question is that if no gas expansion is allowed in that system,what conclusion can I make by equation PV=nRT?
None. By what you said so far, n and V increase in a not-further-specified way. Hence, pressure and temperature can still do pretty much anything. In practice, you might often have the situation that T or P are constant (say because you have your gas in a container through which energy can be transferred (-> system will reach same T as outside) and a mobile container wall exerting no forces by itself (-> same pressure as outside).
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um....i dont know whether my expression about the second question is clear enough.

May I clarifies my second question?

My second question is based on a different situation.In the close system,there is no gas expansion,and no plugs......so even the no. of moles of gas molecules inside the container increases,the volume cannot be changed.

By PV=nRT where R,V are constant,I would like to ask if no. of moles of gas molecules increase,will T,or P is being changed?

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That depends on the type of gas molecules you put in. If you add gas molecules of the same temperature as your gas had, then the temperature will remain the same and P will increase proportional to n. If you you put in n2 mole of the same gas at a different temperature T2, then the resulting temperature will be different. So mathematically, you are then asking what happens to P if V and R are constant, and n and T vary. And the answer is: that depends on how n and T vary. Or put in other words: you simply don't know. That is the mathematically correct answer.

In the real world, say working as a scientist, you are usually not given such abstract questions, but will often encounter such questions in the context of an actual problem, i.e. have a few more information than you gave here. For example, the equation you gave is some state equation for the ideal gas. So in many problems where you use it, you could expect that the equation $E= \frac f2 nRT$ also holds (don't worry about the f, just assume f=3 if you don't know the equation in this form). So if now I add n2 mole of the same substance with a temperature T2, I get a total energy $E' = \frac f2 R(nT + n_2 T_2)$ and a temperature T' of the mixture which is $E' = \frac f2 R(nT + n_2 T_2) = \frac f2 (n+n_2) R T' \Rightarrow T' = \frac{nT + n_2 T_2}{n+n_2}$. So with this not-too-far-fetched additional assumption, you can calculate the new temperature, and therefore know how P will behave. In case you are too lazy to proceed from that point yourself: unless the temperature of the new particles is zero, the pressure will increase (assuming constant volume in all of the above, of course).

I hope it's not too confusing for you. The problem here is that people without a rigorous training in a scientific field tend to formulate problems and solutions in very general ways but at the same time take a lot of assumptions for granted which are not necessarily true. The 1st paragraph of this post is the correct answer to your question. The 2nd paragraph is more likely to be in the line of what you actually wanted to ask, and probably more helpful.

Edited by timo
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In a close system, when no.of mole of gas molecules increase, gas expansion happens, and its plug is being pushed outward.

What i want to ask is that: Where does the energy comes from which does work on the plug?Does the energy come from the vibrational energy or translation energy of the molecules?

Both. All vibrations represent energy, and therefore heat.

The energy for expansion comes from heat in general.

When the gas expands to equalize the pressure on both sides of the plug, the gas cools down (quite a lot!). And in colder molecules, there is less vibration.

Another question is that if no gas expansion is allowed in that system,what conclusion can I make by equation PV=nRT?Will the temperature,or the air pressure inside that system keep constant ?

n increases, and P increases as a result.

In fairness, I am not sure if the temperature would change just because of the creation of more molecules.

The heat of reaction (or: reaction enthalpy) would certainly play a role in changing the temperature. And that in turn has again an effect on the pressure, because of PV=nRT.

Reactions that create more molecules would often be exothermic (combustion, explosion), so the temperature would go up because of the reaction enthalpy.

Hope that helps.

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Thanks for your help!I know what happens there now!

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