Does Volume Increase With Temperature
Why does temperature increase when volume decreases? (Kinetic theory explanations)
- Thread starter eddywalrus
- Starting time engagement
As you do this, the temperature increases, simply why? My best guesses are:
- some of the energy y'all use for pressing downwards on the container is transferred to estrus energy and thus increasing the temperature (?)
- the forcefulness exerted on pushing the container down is passed onto colliding particles, thus increasing their kinetic energy
Only these two explanations would only increase the average kinetic energy by a small corporeality, if at all.
Is there an explanation for this using kinetic theory?
Answers and Replies
If yous compress a gas (say with a piston) the piston will be moving inwards. The molecules that bounciness against it will rebound with a higher velocity (however slowly you do it, y'all will nevertheless go the same answer). This ways they will transfer this increased kinetic energy to all the other molecules. They volition and then exist striking the walls of the container faster. There is more change of momentum at each standoff - so more force - and then more pressure.
Now - the molecules are travelling faster (average speed) so this implies a rise in temperature. If y'all absurd the container down to its original temperature there is Still a different situation, despite the fact that the molecules have the same average speed every bit before. At that place is less altitude for the molecules to travel between collisions with the walls then there will still exist more collisions per 2d. This means that there will STILL exist an increase in pressure.
The "small amount" in your mail service is Just Plenty to produce the right answer. 
If you compress a gas (say with a piston) the piston will be moving inward. The molecules that bounce confronting it will rebound with a higher velocity (however slowly you do information technology, you volition yet get the same answer). This means they will transfer this increased kinetic energy to all the other molecules. They will then be striking the walls of the container faster. There is more alter of momentum at each collision - then more than force - and then more than pressure.
Now - the molecules are travelling faster (average speed) then this implies a ascent in temperature. If yous cool the container down to its original temperature there is Nevertheless a different situation, despite the fact that the molecules accept the same average speed as before. In that location is less distance for the molecules to travel between collisions with the walls so there will still be more than collisions per second. This ways that at that place will Nevertheless be an increase in pressure.The "pocket-sized amount" in your post is Just Plenty to produce the correct answer.
Surely the speed of the compressing piston is negligible compared to the speed of the molecules in the gas?
I would accept thought that the increase in temperature is more likely due to the increased rate of collisions betwixt the molecules...
When the molecules are travelling freely between collisions, they are unlikely to radiate infra-red radiation but can blot infra-crimson radiation. When the molecules collide, they are more likely to release infra-cherry radiation.
When the gas is compressed and the molecules are closer together, their mean time betwixt collisions is less, so there is more infra-carmine radiation beingness released than before the pinch.
The reverse happens when a gas is expanded - the molecules are further apart and their mean fourth dimension between collisions increases, so there is more infra-red radiation being absorbed than before the expansion.
I would have thought that the increment in temperature is more likely due to the increased rate of collisions between the molecules...When the molecules are travelling freely betwixt collisions, they are unlikely to radiate infra-cerise radiations but can absorb infra-red radiation. When the molecules collide, they are more likely to release infra-carmine radiations.
You lot get an increase in temperature even for an ideal gas, in which y'all presume either that the molecules don't interact at all, or that they collide completely elastically without losing kinetic energy. Think, PV = nRT is for an ideal gas!
Yous get an increase in temperature fifty-fifty for an platonic gas, in which you assume either that the molecules don't interact at all, or that they collide completely elastically without losing kinetic energy. Recollect, PV = nRT is for an platonic gas!
How can that be true - that platonic gases collide completely elastically without losing kinetic energy?
For in that case, how would an platonic gas ever lose heat? Since an ideal gas atom (as they are typically mono-diminutive) tin can always absorb an infra-red photon, merely by what mechanism would the ideal gas atom emit an infra-red photon?
An ideal gas does not interact with radiation.
The additional free energy comes from elastic collisions with the compressing wall. Fifty-fifty if the wall moves very slowly, it is far more massive than an atom and the elastic collision will increment the atom'south speed quite a lot (momentum conservation). Since the temperature of a gas is proportional to the foursquare of the rms speed of the molecules, this compression leads to a very noticeable increment in temperature.
eg. for an adiabatic pinch, (T'/T) = (V/V')^(gamma - one)
And so if you lot halve the volume (Five/5' = 2) of a diatomic gas (gamma = seven/5), the temperature will increase by a factor of 2^0.4 = one.32. In terms of Kelvin that's the equivalent of going from room temperature to about 125 C!
"Surely"????Surely the speed of the compressing piston is negligible compared to the speed of the molecules in the gas?
It may seem counter-intuitive simply you won't exist able to show that the statement is incorrect. Remember that every molecule that strikes the piston will have its speed increased by the massive piston. This can happen apace or slowly, depending on the speed of the piston and, withal quickly or slowly the change is fabricated, the KE is redistributed amid all the molecules to produce a different velocity distribution.
The argument to justify Boyle's Law (constant temperature situation) is adequately piece of cake to grasp because it just depends on the reduced corporeality of space and the resulting frequency of collisions. To derive the full Gas Constabulary is a flake more long winded and I recommend that you hunt around on the web for a website that presents it at a level yous tin can cope with. But think of the actual piece of work washed on a gas to compress it to one-half its volume. All that energy has to go somewhere and the just fashion information technology can be transferred for an platonic gas is by speeding up the molecules by contact with the piston.
It has more to do with quantum mechanics, if you lot actually want to talk about it in a way that gets at the fundamental reasons backside it all.
Temperature is a measure of how "spread out" the particles are over all possible energy levels. At low temperatures, the particles are concentrated mostly in the lowest available free energy levels, where as at higher temperatures they're more spread out.
If when y'all compress a volume, you subtract the spacing betwixt energy levels - this is is a issue from breakthrough mechanics.
If you decrease the spacing between energy levels, only don't change the total free energy, then the particles have to spread out and occupy higher energy levels in order to keep everything conserved, and by definition this is a higher temperature.
I think this is really the best manner to retrieve about it.
It has more to do with quantum mechanics, if you actually want to talk about it in a way that gets at the cardinal reasons behind it all.Temperature is a mensurate of how "spread out" the particles are over all possible free energy levels. At depression temperatures, the particles are full-bodied mostly in the lowest available energy levels, where as at higher temperatures they're more spread out.
If when you shrink a book, you lot decrease the spacing between free energy levels - this is is a result from quantum mechanics.
If yous decrease the spacing between energy levels, only don't change the total free energy, then the particles have to spread out and occupy college energy levels in social club to keep everything conserved, and by definition this is a higher temperature.
I think this is really the all-time fashion to think almost information technology.
You are correct, of class simply it may not be necessary to understand this in depth as long as you can take that in that location will be some sort of free energy distribution amongst the molecules. That is a reasonable intermediate step in getting a handle on this, I feel. I realise that QM is necessary to bargain with the 'ultraviolet catastrophe' merely it'southward a huge amount extra to take on board all in one go.
Quote by robinpike
Surely the speed of the compressing piston is negligible compared to the speed of the molecules in the gas?
"Surely"????
It may seem counter-intuitive but you won't be able to bear witness that the statement is incorrect. Call up that every molecule that strikes the piston will have its speed increased by the massive piston. This can happen apace or slowly, depending on the speed of the piston and, however quickly or slowly the change is made, the KE is redistributed amid all the molecules to produce a dissimilar velocity distribution.
The argument to justify Boyle's Constabulary (constant temperature situation) is adequately easy to grasp because it just depends on the reduced corporeality of space and the resulting frequency of collisions. To derive the total Gas Police force is a bit more than long winded and I recommend that you hunt effectually on the web for a website that presents information technology at a level you can cope with. Just think of the actual work washed on a gas to compress information technology to half its volume. All that energy has to go somewhere and the just style it can exist transferred for an platonic gas is by speeding up the molecules by contact with the piston.
Howdy I may be off base merely I run into some questions here.
I understood that ideally slow pinch or expansion was specifically to remove the momentum of the piston from consideration. Equivalent to ideally deadening clock transport to remove time dilation as a gene.
And so for expansion; no work is washed by the gas to remove kinetic energy through transference of momentum to the piston. Or vise versa with compression
Temperature is purely a function of internal kinetic energy so internal collisions are naught sum events and their increase in frequency through decreasing spatial relationships should accept no effect on total energy, although it does have an touch on force per unit area which is dependent on number of collisions with the container walls.
As I recall information technology the increase in internal temperature is related to the Van der Walls force.
As such is a result of spatial reduction and the subtract in the mean altitude between nuclei .
I remember for some monatomic gases, expansion for some pressure ranges actually results in temperature increment. Or reciprocally compression results in temperature decrease which seems to contradict any concept of piston imparted increased velocities.
This force imparts an acceleration to proximate gas molecules dependent on distance then does result in an overall increase in the hateful probable velocity.
If I am wrong in whatsoever of these assumptions I will be happy to learn of it..
I think you may be thinking in terms of isothermal changes or non-ideal gases. It has to exist true that, if you insulate a mass of an ideal gas and do work in compressing it - and in that location is piece of work involved in moving a piston against pressure (force times distance), however slowly yous do it - then conservation of energy must utilise (no?). The only identify the energy can become must be into the internal free energy of the gas. In an platonic gas, this must upshot in an increase in average K.E. - that is an increase in temperature.
When Van der Waall's forces are involved (non-platonic gases), you can get some of the piece of work done transferred to potential energy and that will change the temperature change - in either direction, I seem to recollect.
Look at the Wiki article on Joule Kelvin Effect. They brand the distinction nicely between volume changes with and without work being washed.
Look at the Wiki article on Joule Kelvin Effect. They make the distinction nicely between volume changes with and without work existence washed.
Thanks for the reference . In the meantime I had done some calculation with the increase in gas velocity being 2x the piston velocity per collision.
Doing even a crude quesstimate of the number of collisions based on initial gas velocity and the average length of the container during compression, it was quite articulate that no matter how negligible the piston velocity the internet increment must exist a significant per centum of the initial average velocity, even without considering the exponential increase in collision frequency with increasing velocity.
So I was badly mistaken in my idea of the upshot of wearisome ship and the relative effects of the Van der Wall force.
It makes me wonder virtually the conceptual basis of slow clock transport???
Tin can y'all fool mother nature??
Similar a photon that can popular into beingness out of cipher because information technology happens to quick for the conservation cops to accept action ;-)
Thank you
Glad your sums take convinced y'all about the reasonableness of that. Of form, the actual distribution of velocities later on the alter in volume needs the application of Quantum Theory to avoid the loftier free energy problem.Thanks for the reference . In the concurrently I had done some calculation with the increase in gas velocity being 2x the piston velocity per collision.
Doing even a rough quesstimate of the number of collisions based on initial gas velocity and the average length of the container during pinch, it was quite clear that no affair how negligible the piston velocity the net increase must be a significant per centum of the initial boilerplate velocity, even without considering the exponential increase in collision frequency with increasing velocity.
And so I was badly mistaken in my idea of the issue of slow ship and the relative effects of the Van der Wall force.
Information technology makes me wonder about the conceptual basis of slow clock transport???
Can you fool female parent nature??
Like a photon that tin can pop into existence out of nothing because it happens to quick for the conservation cops to accept activity ;-)Thanks
I think the tedious clock transport thing with light speed is a unlike matter - peradventure to do with the fact that one involves Energy transfer(?).
The faster the molecules are, the more bounces with the moving wall volition occur per time.Surely the speed of the compressing piston is negligible compared to the speed of the molecules in the gas?
The faster the molecules are, the more than bounces with the moving wall will occur per time.
That'due south why both volume and temperature account for the pressure - co-ordinate to the gas laws.
A way to reconcile intuition with sophiecentaur'due south expert caption is to imagine a container of gas at absolute nada, i.e. molecules absolutely at rest. Inserting the piston to shrink the gas leaves particles with motion (increased temp) due to their come across with the inward moving piston. Expansion cannot lower temp below absolute zero because the piston will not collaborate with the stationary gas molecules as it moves abroad.
Interesting, it is possible to "crook" Charle's Police force in the expansion instance if the piston moves very fast, fast plenty that no gas molecules collide with it while information technology is in motion.
In this (impractical) case, the expansion would be simultaneously isothermal and adiabatic.
That's the equivalent of opening the side into a vacuum. No work is done then and then no temperature drop for an ideal gas, I recollect.A way to reconcile intuition with sophiecentaur's good explanation is to imagine a container of gas at absolute cipher, i.e. molecules absolutely at balance. Inserting the piston to compress the gas leaves particles with motion (increased temp) due to their encounter with the in moving piston. Expansion cannot lower temp beneath absolute zero because the piston will not interact with the stationary gas molecules as it moves away.Interesting, information technology is possible to "cheat" Charle'south Law in the expansion instance if the piston moves very fast, fast enough that no gas molecules collide with it while it is in motion.
In this (impractical) example, the expansion would be simultaneously isothermal and adiabatic.
Look at the Wiki article on Joule Kelvin Effect. They brand the stardom nicely between volume changes with and without work being done.
Actually I first encountered this material in the past while researching the basis of compressive cooling. All the literature seemed to agree that such systems worked because gases cooled through expansion. This seemed to me to be a misconception equivalent to h2o as ice cooling through melting. In this instance the ice has non simply less KE than h2o at the aforementioned temp 0 deg C but greatly less internal energy.
And so a system designed to cool the gas itself would be totally adiabatic except for the extraction interface in the compressed phase. It seemed to me that if the free energy extracted was only equal to the free energy added by compression that the system would not piece of work.
Clearly in the case of gases where compression brought about a state transition this made available for extraction a meaning corporeality of internal energy which could so leave the system equally KE or radiation. Then the gas would have a much lower energy content fifty-fifty before the expansion phase.In other cases I understood that extra energy was available for extraction through actualization of Van der Waals potential.
SO if we kickoff with a book of gas, say nitrogen, at environmental temp and bring it down to liquid temperature there is a huge cyberspace loss of energy.
If this energy has non been extracted and now residing in the environment where in fact has it gone???
The ideas that it was somehow "disappeared" through internal throttling seems like energy downwards the rabbit hole.
Or if in that location are two equal volumes with equivalent PT that are expanded into twice the volume, i through throttling and one through free expansion , in the first case at that place is a reduction of temp just not in the 2nd example.(ignoring Van der Waals outcome).
In the beginning example it is stated that there is work done even though there is no exchange with the outside. But if there is no work done on the valve, no transference of momentum, and the final condition is identical to gratis expansion every bit far as deportation of the gas itself where is the result of this work. I.e., where did the energy become??
Thanks
I didn't get the details of all that but when you add all the Kinetic Energies and all the Potential Energies and the Work in or out, the sum will be zero. It'south just a matter of modelling the particular substance right. The devil must be in the particular of the changes of Potential Free energy as the volume changes and the work done. I don't think you can ignore Van der Vaal because that blanket term accounts for the departure from idea l behaviour.
So a system designed to cool the gas itself would be totally adiabatic except for the extraction interface in the compressed stage. It seemed to me that if the free energy extracted was only equal to the energy added by pinch that the system would not work.If this energy has not been extracted and now residing in the surroundings where in fact has it gone???
Thanks
Austin,
I think y'all are missing an important step in your analysis.
First , you are right that when the gas is compressed adiabatically then cooled back to its original temperature, the energy leaving the system in the form of oestrus is equal to the the free energy that was just added in the form of piece of work pushing the piston down. The thermal energy within organization is the same before and afterward since the gas temperatures are the same.
However, in the expansion phase the system is doing work on the environs. Retrieve of it this way: the piston has gas force per unit area pushing outward while the piston is moving outward. This is like a spring expanding, it is releasing energy to the external environs (or amend yet, think well-nigh the gas molecules losing some of their kinetic energy to the outward moving piston at each collision). This is not equally obvious since this rarely represents *useful* piece of work in a cooling system. It is this lost free energy that leads to a lower temperature (and pressure) when we expand back to the original volume.
The PV diagram trajectories for this would be:
1 - compression stage: adiabat upward and to the left.
two - cooling dorsum to original temp: vertical down.
3 - expansion to original volume: adiabat downwardly and to the right.
Your last position will be *below* the original position, i.east. same book, lower force per unit area.
In the reference frame of a wall, when there is an elastic collision between the wall and a small ball then the component of the speed perpendicular to the wall is reversed, assuming information technology wont start rotating. So if you have a ball hitting the wall straight on 5 chiliad/s, it will come dorsum (roughly) at v grand/s. Now if the wall is moving towards the ball at 2 grand/s, the wall sees the ball hitting it at seven m/s and bouncing back at 7 yard/s, merely in the stationary frame you would see the brawl striking the wall at 5 yard/s and billowy back at ix g/southward, and so that's where it gets its extra speed.
In the meantime I had washed some calculation with the increase in gas velocity existence 2x the piston velocity per collision.Thank you
In the reference frame of a wall, when there is an elastic collision between the wall and a small ball then the component of the speed perpendicular to the wall is reversed, assuming it wont start rotating. Then if you accept a ball hit the wall direct on 5 m/s, it volition come back (roughly) at 5 one thousand/south. Now if the wall is moving towards the brawl at 2 m/south, the wall sees the ball striking it at 7 m/s and bouncing back at seven 1000/s, but in the stationary frame you would see the ball hitting the wall at five yard/s and bouncing back at 9 g/s, so that'south where it gets its extra speed.
Thank you for the input but this was already covered. ;-)
A style to reconcile intuition with sophiecentaur'southward good caption is to imagine a container of gas at absolute zero, i.east. molecules absolutely at rest. Inserting the piston to compress the gas leaves particles with move (increased temp) due to their see with the inward moving piston. Expansion cannot lower temp below absolute cipher considering the piston volition not interact with the stationary gas molecules equally it moves away.Interesting, it is possible to "cheat" Charle'south Constabulary in the expansion case if the piston moves very fast, fast enough that no gas molecules collide with it while it is in motion.
In this (impractical) example, the expansion would be simultaneously isothermal and adiabatic.
Hello why would that exist Charles's Police force? In a normal case when i decrease the force per unit area by moving my piston upwards won't the pressure of the gas decrease?
So shouldn't this be a Boyle's Law rather than a Charles'south Law example?
Suggested for: Why does temperature increase when volume decreases? (Kinetic theory explanations)
- Concluding Mail
- Terminal Post
- Last Post
- Last Post
- Last Mail service
- Concluding Post
- Last Postal service
- Last Post
- Last Post
Does Volume Increase With Temperature,
Source: https://www.physicsforums.com/threads/why-does-temperature-increase-when-volume-decreases-kinetic-theory-explanations.648709/
Posted by: mccuskermente1947.blogspot.com
0 Response to "Does Volume Increase With Temperature"
Post a Comment