# Energy stored when compressing a gas

96
When you compress a gas, is 100% (assuming a perfectly efficient motor doing the compression etc) of the energy you expend during compression transferred into extra heat energy in the gas?

2. ### Danger

9,879
Can't be. You can never achieve 100% of anything. For one thing, part of that heat will radiate through the container and attachment line. The losses even go so far as to include outgassing, where some of the gas molecules manage to seep through the walls.

### Staff: Mentor

Actually, losses are generally all heat, but in this case the answer is so obvious that I'm not sure the question is worded correctly: If all the energy expended went into heat, there'd be no compression. Assuming that's not what was meant, some of the energy expended goes into compressing the gas and some is lost as heat by the motor/pressure efficiency. In addition, any heat generated by the compression (via the ideal gas law) may be lost, depending on the specifics of the situation.

4. ### Q_Goest

2,967
Great question, the answer is a bit counter intuitive. But first you need to make some assumptions.

Assume:
1) 100% isentropic efficiency
2) Heat Added = heat required to reduce discharged gas back to inlet temp.
3) No mechanical losses in compressor
4) No unrecoverable pressure losses in any portion of the flow stream

Needless to say, those are some rather broad and unrealistic assumptions, but what it says is that, with the exception of losses due to friction or other mechanical or fluid losses, we will compare the power needed to compress a gas isentropically to the energy removed to return the flow to the original temperature after compression.

I checked the results of this using a computer program that I use all the time where frictional and other losses can be added. I simply removed all losses to calculate the following.

Depending on the gas, the heat removed may be higher, equal to, or lower than the power required to compress the gas. They will be roughly the same.

In real life, losses typically result in more power being needed than is removed.

If you make different assumptions, the answer will also change.

96
I'll attempt to re-phrase. Lets say you have a syringe blocked off at the needle end, fully let out, filled with air. If you put 1000 J of energy into the syringe , by applying a force of 1000N over 1 meter (arbitrary numbers, average force) would the internal heat energy of the air inside the syringe increase by 1000 J? I'm just trying to make sure there isn't anything I'm forgetting.

But I think Q_Goest affirmed my assumption. Thanks.

96
Or is there some other form of energy (potential?) that the 1000N force over 1M goes into?

7. ### rachmaninoff

0
In the ideal case, the internal energy would increase by 1000J; this goes into the K.E. of the gas molecules, causing an increase in temperature. "heat energy" is meaningless - heat is a form of energy transer, a change in energy caused by 'heating' something (putting it in thermal contact with something with a higher temperature). In your example, the only method of energy transfer is mechanical compression, a type of work.

8. ### BlueWaterGuy

3
Are there any formulas to actually calculate to know if the energy in a cylinder of compressed gas/s (air) contains more energy or less energy than was used to compress it. doe is depend on nature of gas being compressed. A cylinder of compressed O2 by itself clearly would have a higher energy content than the energy consumer in compressing it, right. But I don't get the sense, and can't calculate the energy in a cylinder of compressed air, a mixture of gases. Any Ideas or formulas out there?

9. ### BlueWaterGuy

3
Hi there,
Are there any formulas to actually calculate to know if the energy in a cylinder of compressed gas/s (air) contains more energy or less energy than was used to compress it. doe is depend on nature of gas being compressed. A cylinder of compressed O2 by itself clearly would have a higher energy content than the energy consumer in compressing it, right. But I don't get the sense, and can't calculate that the energy in a cylinder of compressed air is less or greater every time, if it depends on variables and assumptions what are the basic assumption in addition to the ones you've mentioned. Is this because there are so many variables. I'm trying to calculate if there is consistently, in all cases, less energy in the compressed volume then energy expended and lost in the performance of the compression. What is the basic calculation beyond thermodynamics. Are there any formulas out there? oh yea I'm not an eng., you may be able to tell. any guidance or information will be helpful.

### Staff: Mentor

You can start with the ideal gas law: pv=nrt. Or you can read the energy numbers directly from a table of those gas properties. Here's one:

http://www.fing.edu.uy/if/mirror/TEST/testhome/Test/solve/basics/tables/tablesIG/igAir.html
I'm not exactly sure what you mean by that. Are you looking for the fraction of energy dissipated as heat and the fraction that is stored in the compression? Or are you trying to compare one gas to another?

You said you aren't an engineer, but I doubt that the first couple of chapters of an engineering thermodynamics book are beyond your grasp - you may want to buy/borrow one. Here's an animation of one way to model this: an isothermal process: http://lorien.ncl.ac.uk/ming/webnotes/Therm1/revers/isothe.htm

Last edited: Oct 22, 2009