Gas compression - does it double the energy?

[RichMacf]

It takes energy to compress an ideal gas, and that same amount of energy is output as heat. But we also gain the potential energy of the compressed gas. It seems to me that we are doubling up our energy.

Can anybody explain in simple, practical terms (to a humble mech engineer) how this works. It’s like having our cake and eating it! I know the theory and calculations, but I still can’t get my brain around the principles.

Isothermal and adiabatic compression both produce heat, but we remove it during the compression, or cooling the hot gas after. If our motor was driving a simple friction brake we would just get heat, but if it’s driving a compressor we get the heat and the potential energy.I’m working on compressed air energy storage, and these are my calculations. For 1kg of air, isothermal compression to 100 Bar takes 387 kJ of energy, and the same 387 kJ of heat is output. For adiabatic, the work is 573 kJ, and the intercooler would take out 573 kJ from 1092K to ambient.

 

[Chestermiller]

It takes energy to compress an ideal gas, and that same amount of energy is output as heat. But we also gain the potential energy of the compressed gas. It seems to me that we are doubling up our energy.

Can anybody explain in simple, practical terms (to a humble mech engineer) how this works. It’s like having our cake and eating it! I know the theory and calculations, but I still can’t get my brain around the principles.

Isothermal and adiabatic compression both produce heat, but we remove it during the compression, or cooling the hot gas after. If our motor was driving a simple friction brake we would just get heat, but if it’s driving a compressor we get the heat and the potential energy.I’m working on compressed air energy storage, and these are my calculations. For 1kg of air, isothermal compression to 100 Bar takes 387 kJ of energy, and the same 387 kJ of heat is output. For adiabatic, the work is 573 kJ, and the intercooler would take out 573 kJ from 1092K to ambient.

In isothermal compression, the internal energy U doesn't change at all. This certainly doesn't double up its internal energy (or its potential energy, whatever you mean by that term).

In thermodynamics, absolute internal energy is never a consideration in practice. Only relative changes in internal energy are important.

 

[jack action]

For 1kg of air, isothermal compression to 100 Bar takes 387 kJ of energy, and the same 387 kJ of heat is output.

So you input 387 kJ into a system, the system cannot store this energy so it outputs it entirely. That seems logical to me. You "gain" the energy from the compression, but you "lost" the same quantity of energy as heat. But that same heat transfer produced an energy gain for the surrounding area though. It's all about clearly identifying your control volume.

Imagine doing the reverse process, decompressing the gas, but without adding heat to it. You would go back to the initial volume and pressure, but your temperature would be lower. That is proof that your system lost energy during the heat transfer.

 

[erobz]

It takes energy to compress an ideal gas, and that same amount of energy is output as heat. But we also gain the potential energy of the compressed gas. It seems to me that we are doubling up our energy.

Can anybody explain in simple, practical terms (to a humble mech engineer) how this works. It’s like having our cake and eating it! I know the theory and calculations, but I still can’t get my brain around the principles.

Isothermal and adiabatic compression both produce heat, but we remove it during the compression, or cooling the hot gas after. If our motor was driving a simple friction brake we would just get heat, but if it’s driving a compressor we get the heat and the potential energy.

Adiabatic compression is without heat transfer out of the gas...during the compression. So, if you take a gas of some volume and compress it, the work that you did on the gas to compress it is absorbed by the gas...at least temporarily. As @Chestermiller points out, for isothermal compression the work you did to compress the gas leaves the gas as heat during the compression, thus no change in internal energy between initial and final states.

 

[Lnewqban]

Welcome!

 

[Steve4Physics]

It takes energy to compress an ideal gas, and that same amount of energy is output as heat. But we also gain the potential energy of the compressed gas. It seems to me that we are doubling up our energy.

Can anybody explain in simple, practical terms (to a humble mech engineer) how this works. It’s like having our cake and eating it! I know the theory and calculations, but I still can’t get my brain around the principles.

Hi @RichMacf. Welcome to PF.

In addition to the other excellent replies, can I add this…

Your confusion arises because there is, in fact, no gain in potential energy.

The internal energy of an ideal gas is simply the total kinetic energy of its particles. There are no inter-particle forces for an ideal gas - so there is no ‘potential energy’ associated with such forces.

The internal energy of an ideal gas depends only on the number of particles and the temperature.

For example: you compress 1 mol of ideal gas at 300K from 100cm³ to 1cm³ and then cool the compressed gas back to 300K.

The initial and final internal energies of the ideal gas are exactly the same.

(The above is not true for a real gas - because of the inter-particle forces - but may be an adequate approximation sometimes.)

 

[Lnewqban]

Please, see:
https://www.engineeringtoolbox.com/horsepower-compressed-air-d_1363.html

When high pressure air is needed, pressure and dryness are good, but the increasing temperature is an undesired consequence for the metals and lubrication.
The input shaft provides the work for both, increased pressure and temperature.

When the compressed air is cooled down, pressure is reduced some and contained humidity tends to precipitate inside the pipes and tanks; which then needs to be removed.
The cooling agent takes away some of that input shaft work.