Temperature: Intensive Property Explained

[Esfand Yar Ali]

Can anyone tell me about how temperature is an intensive property.Intensive properties are roughly those which do not depend on the size of the system or amount of matter in the system,but temperature does depend on amount of matter because it has a relation with pressure also,and pressure depends on the amount.I'm talking about the internal pressure here

 

[phinds]

If you have a pan of water at, say 200 degrees F, and your remove a ladle-full, does the rest of the water change temperature?

 

[Sturk200]

here

The way I think of it is to ask whether the quantity scales with particle number, holding all else constant. So, as per phinds, take a system at some temperature, hold pressure and volume constant, and change the particle number. Does the temperature change? No. Compare this to, for instance volume, which is an extensive property. Take a system which occupies some volume, hold pressure and temperature constant, and add or remove particles. Does the volume change? Necessarily yes.

 

[Khashishi]

Sturk, you made an error there which I hope was just a typo. The first example you have is wrong; you can't change particle number while holding all those things constant.

Esfand, you have to be careful about what you mean by "depends on" in thermodynamics. The equation of state relates several quantities together, and so they all depend on each other. You can talk about the dependence of any two quantities while holding the other quantities fixed. For example, for an ideal gas, temperature depends on number of moles if I hold volume and pressure fixed. But it is ambiguous to say temperature depends on number of moles without saying what I do with volume and pressure. If I let volume increase proportionally as I increase the temperature, then temperature doesn't depend on number of moles. It's all about the context.

An intrinsic property can be thought of as an average value at any point in the system, whereas an extrinsic property isn't and is usually some kind of total of the entire system.

 

[nasu]

Can anyone tell me about how temperature is an intensive property.Intensive properties are roughly those which do not depend on the size of the system or amount of matter in the system,but temperature does depend on amount of matter because it has a relation with pressure also,and pressure depends on the amount.I'm talking about the internal pressure here

The pressure is an intensive property too. It does not depend on the size of the sample.
If you divide a chamber with uniform pressure into two (with a divider), the pressure in each half will be unchanged. So your reasoning relies on a wrong assumption.

 

[Sturk200]

Sturk, you made an error there which I hope was just a typo. The first example you have is wrong; you can't change particle number while holding all those things constant.

As a matter of fact, that was not a typo, but a brain-o. I resign.

 

[Esfand Yar Ali]

okay,now consider this. I've say 50 molecules of any gas in a chamber ,and because of their collisions ,they'll have a particular pressure and thus temprature in the system.Now , if remove 30 molecules from it ,the pressure will decrease ,but what will happen to the temprature?

 

[jtbell]

What do you think, and why? If you're assuming an ideal gas, consider PV = NkT. Is P the only quantity that decreases?

 

[Khashishi]

You have to specify how you remove the 50 molecules

 

[Esfand Yar Ali]

Can I say that because of the removal of 30 molecules,the pressure will decrease but so as the volume,thus temperature will remain constant?

 

[phinds]

Can I say that because of the removal of 30 molecules,the pressure will decrease but so as the volume,thus temperature will remain constant?

Why would the volume decrease?

 

[Esfand Yar Ali]

Why would the volume decrease?

Yes,the volume will ot decrease in the first place.Then how is it explained

 

[ehild]

Can anyone tell me about how temperature is an intensive property.Intensive properties are roughly those which do not depend on the size of the system or amount of matter in the system,but temperature does depend on amount of matter because it has a relation with pressure also,and pressure depends on the amount.I'm talking about the internal pressure here

Intensive and extensive properties are related when you make a system of more identical ones.
Assume you have two identical vessels of water, with volume of 1 L and the same temperature, 20 °C. You put the vessels together and remove the wall between them. The new system has twice the volume of the original ones and the same temperature as the original ones. Volume is extensive property as it is multiplied when making a new system from more identical ones. The temperature does not change: it is an intensive property.

 

[gracy]

Beautiful answer. Thanks @ehild

 

[ehild]

The same works for gases.
You have a cylinder divided by a thin wall at the middle which separates it into two identical chambers of 1 m³ volumes. Both chambers are filled with 1 mol O₂ gas at identical temperature of 300K. You remove the wall, so you have 2m³ volume of 2 mol of O2 gas, at the same temperature. Temperature is intensive property, volume and mol number are extensive properties.

What about the pressure? It depends on the volume and number of moles, according to PV=nRT.
The pressure in both the 1 m³ chambers is P=nRT/V=(1mol)*R*(300K)/(1m³)=300R.
The pressure in the united system is P=(2mol)*R*(300K)/(2m³ )= 300R.
Pressure is also an extensive intensive property, it does not change if you unite identical systems.

 

[Khashishi]

You mean pressure is an intensive property

 

[gracy]

You mean pressure is an intensive property

Yes. Pressure and temperature are intensive property.

 

[ehild]

You mean pressure is an intensive property

Yes, I corrected it now.