# Tempreature Rise In Gases On Compression

1. Oct 14, 2009

### RohansK

This is actually related to Thermodynamics but as it comes directly under the Mechanical field I'm asking it here and I invite all my fellow Mechanical Engineers and Physics Experts to answer this.

The question is : How does the Tempreature of a gas change (increase) when the gas is compressed

Consider an Isentropic Compression

Now what we learned in the Thermodynamics books was that as a gas is Compressed the weight on the piston did the Work On the gas. As a result of the work interaction the system ie the gas gains energy and the tempreature of the gas rises due to increase in the internal energy of the molecules.

As far as this explaination goes it sounds OK but lets go a little deeper on the atomic/molecular level. We shall first see the Assumptions made in th famous Kinetic Theory Of Gases for the above explaination.

Assumptions of Kinetic Theory Of Gases :

1. The collisions between the molecules are perfectly Elastic like two solid spheres colliding with each other. ----------- OK Accepted.

2. The Velocity of a molecule does not change between two succesive collisions ie its Kinetic Energy also remains constant between two collisions. --------- OK Accepted.

3. There exsists No Force of Attraction or Repulsion between the molecules when they collide ie there is No Interatomic Forces between them at all. --------- OK Accepted.

When we agree to the assumptions and the Ideal Gas Law ( PV = mRT) together and then think about how the gases behave on compression then two questions arise to me.

1. Consider the case when a gas in a cylinder is compressed by the piston forced inwards. And let the process be achieved very slowly ie Quasti Static.
Let there be 'n' number of moleucles in volume V1 at pressure P1 and tempreature T1. When the gas is compressed the volume reduces to V2 the presssure rises to P2 and the tempreature increases to T2.
Now as the tempreature rises to T2 it is clear that the internal energy has rised. It means that the Kinetic Energy of the gas molecules has increased ie their Velocity has increased.

Note that when the gas was at state1 assume the molecules had a mean velocity u1 and the number of molecules per unit volume were n/V1. The tempreature if measured would be proportional to the number of molecules in contact with the thermomoeter bulb and their summation of average Kinetic Energy they transfer to the bulb.

Keeping this in mind when the gas is compressed to volume V2 the number of molecules per unit volume would increase to n/V2. And n/V2 is > n/V1.
Also there is no heat source to add to the energy of the molecules and neither is any visible effect of gaining energy through impact of the piston with the molecules during compression because the process is very slow ie Quasi Static so impact/striking and transfering KE is ruled out. So there is no direct souce to increase the KE or Velocity of the molecules.
But as we note that the tempreature has increased we say that the KE or the velocity of the molecules also has increased. But there is NO SOURCE to make this effect. So if there is no visible source or reason to rise the KE of the molecules how does the tempreature rise.
Also the number of molecules in contact with the thermometer bulb would now be much more than the first case. And as the tempreature shown is greater but there is NO REASON visible which may have increased the KE or velocity of the molecules can we say that the sole reason of tempreature rise is the rise in number of molecules in contact with the bulb and that there is no contribution of any rise in KE of the molecules in state2 to the rise in tempreature.
Can anyone explain this. As to satisfy the fact that as tempreature rises the internal energy also rises.
Where does this rise in internal energy come from.

I know some may say its the Work Done by the piston but I think the piston does only the job of resisting the higher pressure ie opposition created by the gas during compression.

Secondly what my thought is ( which I want to actually confirm here and discuss) is as follows :

I think the rise in the tempreature of the gas is due to the fact that as the gas is compressed its volume decreases. So the molecules which are seperated by greater distances earlier start to come closer now. As the gas is compressed further to such volumes where the seperation between them and the size of the molecules become comparable there will Exsist a strong Intermolecular Force of Attraction and Repulsion between them as they approach each other during a collision.

Hence when two molecules come closer they start attracting each other with increasing force of attraction wrt to closing in distance and when they surpass the mean seperation (state of equilibrium positon between atoms) the repusive forces start to act with much greater intensity of force per unit distance as compared to the attractive forces. This will certainly INCREASE the KE and VELOCITY of the molecules as the Forces acting on them have increased in magnitude. So the molecules will vibrate/collide with greater velocities now as compared to state1.
Combining this effect with the fact that the number of molecules per unit volume n/V2 is greater than n/V1 the space being confined the seperation between the molecules will decrease giving rise to the above discussed forces coming in action which will naturally increase the KE and velocity of the molecules. This explains or satisfies the factual condition that Internal Energy ie KE ie Velocity of the molecules rises when the tempreature rises from T1 to T2 after compression.

This rise in KE of the molecules could not be explained by the Kinetic Theory alone which assumed the collisions perfectly elastic and Velocity of molecules remaining constant between collisions ( except when heat added).

Is this thinking of mine correct. If not HOW WOULD YOU EXPLAIN THE INCREASE IN KE OF THE MOLECULES A THE TEMPREATURE RISES.
And is rise in tempreature only a function of increase in number of molecules per unit volume ( actually number of molecules in contact with the bulb of thermometer) alone and that there is no rise in the KE of molecules in accordance to Kinetic Theory Of Gases.

- Regards and Thanks.

Last edited: Oct 14, 2009
2. Oct 14, 2009

### Mapes

No, you can't rule out the transfer of momentum from the moving piston. The slower you move the piston (at nonzero speed), the longer the entire process will take. In the end, you've transferred the same amount of energy to the gas, by giving a small "kick" a huge number of times to a huge number of molecules.

3. Oct 14, 2009

### tyroman

Another way to look at it...

Assume you have a vertical cylinder, open at the top and full of gas at 1 atm. Now, fit a massive piston into the top of the cylinder and allow it to move downward due to the force of gravity. As the piston gets closer to the center of the earth, its gravitational potential decreases.

As the gas is compressed, its temp rises due to an increase in KE of the gas molecules. The increase in KE of the gas is exactly equal to the loss in PE (gravitational potential) of the piston. (Neglecting friction, etc. etc.)

All the above is based in Classical Mechanics...

Where you say:

"Secondly what my thought is ( which I want to actually confirm here and discuss) is as follows :"

you are entering the realm of Quantum Mechanics... where Classical Mechanics breaks down and different formulas / rules apply.