# Compression due to temperature rise vs volume reduction

1. Oct 20, 2015

### escape_velocity

If I have 2 sealed tanks A and B of 1 cu ft volume that contain air at atmospheric pressure and are at 300 deg K. temp absolute.

For tank A I raise the temperature from 300K to 600K and I suppose the pressure will double due to this and would be 14.7 * 2 = 29.4psi absolute

For tank B I use a piston and compress the air in it to 29.4 psi. I don't really know how to calculate the heat of compression in this case.

Now If I allow both tanks to cool to ambient.
Would the pressure in both tanks reduce to atmospheric pressure?

What is the fundamental difference between the pressure increase due to temperature and and pressure increase due to mechanical compression?

2. Oct 20, 2015

### BvU

Tank B has double pressure.
See ideal gas law.

In tank B the compression process "can" be done reversibly and then it follows the ideal gas law. The gas gets twice as hot from the work you do on the piston.

3. Oct 20, 2015

### escape_velocity

1. Why would Tank B NOT return to the original pressure of 14.7 psi?
2. By reversible compression did you mean isothermal compression?

4. Oct 20, 2015

### Staff: Mentor

This is not correct. For adiabatic reversible 2x compression of an ideal gas, the temperature ratio is $2^{\gamma -1}$, where $\gamma$ is the ratio of the constant pressure- and constant volume heat capacities.

5. Oct 20, 2015

### Staff: Mentor

Are you currently taking a course in physical chemistry or thermodynamics? If so, you are probably getting ahead of your current course material. Material like this will be covered later. For now, you are probably learning about the ideal gas law, correct? My advice: just use that for the present to answer the questions that it can address on its own, and wait until later to see how it is applied to more complicated problems.

Chet

6. Oct 20, 2015

### escape_velocity

But I really do need to understand this topic, could you kindly explain the true difference between pressure rise due to temperature and pressure rise to do mechanical compression. Even a clue or a reference would do. I would refer to it and then get back if necessary.
Many thanks.

7. Oct 20, 2015

### Staff: Mentor

BvU gave you a good answer at one level, but apparently that was beyond where you are now. Please tell us what level you are approaching this from. For example, are you familiar with the first law of thermodynamics? Do you know what internal energy is? You apparently have never heard the term reversible process. Are you familiar with the term adiabatic process? We need to know this so that we can properly answer you at a level you can understand.

Chet

8. Oct 20, 2015

### gmax137

what does mechanical compression do to volume?

9. Oct 20, 2015

### escape_velocity

it reduces it?

10. Oct 20, 2015

In a container the rapid motion and collisions of molecules with the walls of the container causes pressure (force on a unit area).Where the motion of molecules depend on temperature.So, the more you rise temperature the more pressure rises.
Mechanical comparison is more simple than that comparison of temperature.Its just an equalization process. When you blow air into a balloon, the balloon expands because the pressure of air molecules is greater on the inside of the balloon than the outside. Pressure is a property which determines the direction in which mass flows. If the balloon is released, the air moves from a region of high pressure to a region of low pressure and the balloon deflates.

11. Oct 20, 2015

### BvU

My mistake: I did indeed mean reversible isothermal (it's easier on the math) and then the work you do is heat given off to the surroundings. So the gas doesn't get twice as hot.

To be honest, I completely oversaw what Chet points out.

12. Oct 20, 2015

### gmax137

Right. So, do you know the ideal gas law, and what it says about volume, pressure, and temperature?

13. Oct 20, 2015

### Staff: Mentor

So how can a vessel with a permanently reduced volume return to its starting conditions?

14. Oct 20, 2015

### escape_velocity

I am familier with these terms. You could freely use them in your answers.

15. Oct 20, 2015

### escape_velocity

PV = nRT
In mechanical compression
V would reduce
P would go up
T would go up

16. Oct 20, 2015

### escape_velocity

If a vessel is permanently reduced volume that is if it is a rigid container. I suppose it would never return to starting conditions.
Are you referring to Tank A the one that we are giving heat to?

17. Oct 20, 2015

### Staff: Mentor

OK. So, if you are familiar with all that, please describe in words (qualitatively) what happens in the adiabatic compression of a gas in terms of the heat added to the system, the change in internal energy, and the work done by the system on the surroundings. Then write for us an equation that applies the first law to the adiabatic compression of a gas.

Chet

18. Oct 20, 2015

### ogg

Escape. In school we usually start with the various gas laws PV=k, P/T = k, P=nk, etc. and come to the Ideal Gas Law PV=nRT. Why? because it is so useful and general.
will heat up as they are crowded...NOT something point-like particles need be concerned with.) (In other words, the fact that a gas changes T as it expands or is compressed is PROOF that atoms (molecules, actually) are not point-like and/or do interact.) Elementary thermodynamics deals with situations where gravity, the weak force, strong force, and even most electromagnetic radiation can be (and is) ignored. (Just picture a tank 1000km high, think pressure will be uniform?? (and how about Temperature? Will T EVER become uniform????!?!(hint: velocity is a measure of kinetic energy = molecular heat, and escape velocity is the velocity at which gravity is "overcome"...). Further information on how T of a gas increases with energy (work, heat) can be found under Heat Capacity in Wikipedia, but reading through it requires a bit of partial differentiation (of simple multivariate equations, f(x,y,z)) which may be something you've not learned yet...(check out the section on diatomic gasses).

19. Oct 20, 2015