# Cold air vs hot air in turbochargers

1. Apr 8, 2009

### darkdrifter04

Okay so i have a project, and this is pretty basic physics but i'm kind of confused. so for those of you how a turbo work, please help me out here. okay so:
pV = nKT in thermodynamics.
so in a turbo, as air enters the compressor turbine, n and k stay constant correct? however as air enters the system, volume decreases when it enters the turbine, and as a result pressure increases. however, since volume decreases, shouldn't temperature increase since there is less space and thus molecules collide more? i don't understand it, because in the equation pv=nkt, if n and k are constant, then an increase in pressure or an increase in volume should mean an increase in temperature. doesn't make sense, can someone clarify that?

also i was wondering why, when pressure of the air increases, density of the air increases as well, is there an equation? for example like 15 psi is less dense than 20 psi of boost. why is that? (if you think your helping me too much, is there a name for it?)

thanks!

2. Apr 8, 2009

### Staff: Mentor

I don't get what you don't get. The compressed air gets hot, that's why you use intercoolers.

Besides, it is R, not K.

As for density - mass and number of moles are directly proportional, you should be able to calculate density using PV=nRT and mass=n*molar mass formulas.

3. Apr 8, 2009

### Arjan82

In your case V is smaller and P becomes bigger, however temperature would only stay the same if the product of P times V stays the same. This, however does not happen. P increases much more than V decreases and thus temperature increases

4. Apr 8, 2009

### Bob S

Should air in turbochargers follow the adiabatic rule P V1.4 = nKT, like it does in other air compressors? If air did not heat as it is compressed, diesel engines would not work.

5. Apr 8, 2009

### Arjan82

To see why the temperature in a gas rises due to compression you need the first law of thermodynamics:

dU = dQ + dW

In words: the incremental increase in internal energy U equals the heat added (dQ) and the work done to the system (dW). Now, since for an ideal gas it can be shown that dU = C_v * dT (C_v is the heat capacity at constant volume, dT the temperature increase). Furthermore, let's assume no heat is added to the system. And dW = -p dV, thus the work done equals the change in volume times it's pressure, so:

C_v * T = -p dV

For compression dV is negative and so the increase in temperature is positive, the air gets hotter.

6. Apr 8, 2009

### Physics_Kid

so Arjan82 answerd the increase in temp question.

let me clarify some statements about the turbo. there is no "compressor turbine". a turbo has a compressor on one side and a turbine on the other side. the turbine removes energy from the hot moving exhaust and transfers that energy over to the compressor wheel wherby the compressor wheel compresses the air.

and to answer the density question, density is directly related to the mass and volume. mass has a direct relationship to the # of molecules via molecular weight. if you know the density then for any given volume the mass and # of molecules can be calculated, etc.

7. Apr 8, 2009

### Arjan82

The relationship you are looking for is $$p = \rho R T$$, called the gas law which is valid for air in by far most situations. p is pressure $$\rho$$ is density, R is a constant and T is temperature in Kelvin. This formula simply states that when pressure increases, density increases as wel provided that the temperature doesn't increase too much as well.

Let's define too much. If you would pump the tire of your car, you are raising the pressure from 1 bar to, say 2 bar, to keep things easy. Say you would like to keep the density the same, in that case you should double the temperature. Keep in mind the temperature is in Kelvin! Thus on a normal day it could be like 293 degrees kelvin, to keep the density the same you would need to raise the temperature to 586 degrees kelvin! or 313 degrees Celsius! or 595 degrees Fahrenheit! (which ever system you prefer). This is quite a big increase in temperature to raise the air in a tire to just two bar.

So for your question, 15psi boost is less dense than 20 psi boost, provided that the temperature is about the same... To see the link between pressure temperature and density: pressure is nothing but a measure for how hard and how often an air molecule hits some wall. Temperature increases the kinetic energy and thus the average speed of the randomly moving molecules and density has an influence on how often a molecule is likely to hit that wall. Higher density means more molecules in the same room and thus the wall will be hit more often.

Last edited: Apr 8, 2009
8. Apr 8, 2009

### Arjan82

darkdrifter04 has got the formula right. R=N_a * k / M , with N_a is Avogadro's number and M the (average) molecular weight. n in darkdrifter04 stands for the number of molecules. In your formula PV=nRT, it stands for number of moles.

9. Apr 8, 2009

### Staff: Mentor

So it should be nkT, not nKT

10. Apr 9, 2009

### Arjan82

Okok, k stands for the Boltzmann constant, should not be capitalized indeed :)

11. Apr 12, 2009

### darkdrifter04

oooo got it, thanks all :)