B Comparing energy released to the energy needed to compress a gas (game design scenario)

[Ax_xiom]

TL;DR Summary

Given you want to compress 2600 cubic centimeters of air so it expands with 1.7e26 joules, how much energy do you need to put into compressing the air?

So I was looking at this post and was questioning the physics behind it.

The jist is that the person in the post claimed that to compress 2600cm³ air enough so it expands with 1.7*10²⁶ joules you'd need to actually apply 7.8*10²⁸joules to compressing the air because energy is lost due to heat and friction

But I'm a bit confused as I don't think air works like that. Whether the air was compressed adiabatically or isothermically the air will expand with the same amount of energy assuming the expansion is also adiabatic/isothermic.

I asked him for his reasoning and he told me to look it up before subsequently blocking me (bad sign)

So who's right and what's the actual science behind this?

 

[Chestermiller]

Well, I don't know what kind of compression and expansion processes you are referring to, but if the compression and/or expansion is not done very slowly (i.e., reversibly), then part of the mechanical work energy is transformed to internal energy of the gas by way of its viscous nature. Apparently unbeknownst to you, air is a viscous fluid, and high rates of deformation of this viscous fluid result in conversion of mechanical energy (work) to internal energy.

 

[Ax_xiom]

then part of the mechanical work energy is transformed to internal energy of the gas by way of its viscous nature

Ok that makes sense, is it possible to calulate or at least estimate the energy transformed into internal energy and not done on the environment when the air expands?

 

[The Fez]

Reading the reddit thread, there is no way to calculate this at all, based on the amount of power we're dealing with (about 3 billion times the total power consumed by everyone on earth in a year), compressed into such a small area (at least fusion level temperatures, probably greater than CERN level energy densities). The person posting those numbers is obviously throwing out random numbers. On a normal scale, if you want to calculate the energy efficiency of a reasonable amount of energy, there is a lot being done on compressed gas energy storage, and you could look up the round trip efficiencies stated. I'm sure its much greater than the 0.2% stated by Reddit poster.

 

[Ax_xiom]

Reading the reddit thread, there is no way to calculate this at all, based on the amount of power we're dealing with (about 3 billion times the total power consumed by everyone on earth in a year), compressed into such a small area (at least fusion level temperatures, probably greater than CERN level energy densities).

Yeah, I did some rough estimations and the particles will have around one billion times the energy of particles in the Large Hadron Collider. Such energy densities should result in some uber exotic form of quark gluon plasma with tons of particles being spontaneously created and stuff.

On a normal scale, if you want to calculate the energy efficiency of a reasonable amount of energy, there is a lot being done on compressed gas energy storage, and you could look up the round trip efficiencies stated. I'm sure its much greater than the 0.2% stated by Reddit poster.

I remember looking at that (I even quoted my findings to him before he blocked me) and the lowest efficiency I was able to find was like 10% and on average they're around about 65% efficient.

 

[Chestermiller]

Ok that makes sense, is it possible to calulate or at least estimate the energy transformed into internal energy and not done on the environment when the air expands?

Yes, this can be done, but to do so, you need to perform fluid dynamic, mass balance, and energy balance developments on differential sized (spatial) elements of gas within the system, and solve the resulting set of partial differential equations (and boundary conditions) for the spatial and time variations of pressure, gas velocity, temperature, and density throughout the gas. This will enable you to determine the rate of entropy and internal energy generation as a function of time and position.

Such calculations are usually done using computational fluid dynamics (CFD).

 

[snorkack]

As for permanent loss of energy, consider that energy spent on heating the air by viscous friction is recoverable on expansion. Energy gets lost when it is removed from the hot air by conduction or radiation, which depends on the goodness of heat insulation. Or when it is spent on endothermic reactions that are not easily reversed.

Air is nitrogen and oxygen.
At high temperatures, a portion of the nitrogen and oxygen react to form nitrogen monoxide. This reaction loses energy. At all temperatures, the equilibrium amount of nitrogen monoxide is a minority.

As the temperature drops, the equilibrium amount of nitrogen monoxide drops... but the reaction speed also drops, so the reaction freezes out. Temporarily heating air by flame or adiabatic heating and cooling it back loses some heat and therefore work on fixing nitrogen. And nitrogen monoxide is stuff you do not want in many places even if you could afford the energy.

I assume the actual loss of energy on NO generation is a minor issue compared to the other problems NO makes. Can anyone offer quantitative estimates on energy spent (unintentionally) on NO?

 

[Ax_xiom]

Yes, this can be done, but to do so, you need to perform fluid dynamic, mass balance, and energy balance developments on differential sized (spatial) elements of gas within the system, and solve the resulting set of partial differential equations (and boundary conditions) for the spatial and time variations of pressure, gas velocity, temperature, and density throughout the gas. This will enable you to determine the rate of entropy and internal energy generation as a function of time and position.

I'm now 100% convinced the person in question was lying about doing the calculations as solving a series of partial differential equations and finding all the variables needed (especially all we have are a few manga panels) isn't something you can look up in half an hour (unless you have a degree in fluid dynamics and then you wouldn't say stuff like "joules of force")

Such calculations are usually done using computational fluid dynamics (CFD).

And I would assume such models break down with plasma with quarks moving with energy densites a billion times that in the LHC.

 

[Chestermiller]

As for permanent loss of energy, consider that energy spent on heating the air by viscous friction is recoverable on expansion.

It cannot be recovered by any process which returns both the system and surrounding to their original state, unless the original process is reversible. This is a consequence of the 2nd law of thermodynamics.

Air is nitrogen and oxygen.
At high temperatures, a portion of the nitrogen and oxygen react to form nitrogen monoxide. This reaction loses energy. At all temperatures, the equilibrium amount of nitrogen monoxide is a minority.

As the temperature drops, the equilibrium amount of nitrogen monoxide drops... but the reaction speed also drops, so the reaction freezes out. Temporarily heating air by flame or adiabatic heating and cooling it back loses some heat and therefore work on fixing nitrogen. And nitrogen monoxide is stuff you do not want in many places even if you could afford the energy.

I assume the actual loss of energy on NO generation is a minor issue compared to the other problems NO makes. Can anyone offer quantitative estimates on energy spent (unintentionally) on NO?

The NO concentration within atmospheric air is tiny, and insignificant to the energy balance for the air. See

Miller, C., Meakin, P., Franks, R.G.E., and Jesson, J.P., The Fluorocarbon-Ozone Theory – V. One Dimensional Modeling of the Atmosphere: The Base Case, Atmospheric Environment, 12, 2481-2500 (1978)

 

[Chestermiller]

And I would assume such models break down with plasma with quarks moving with energy densites a billion times that in the LHC.

The OP strongly implied air at conditions not grossly removed from typical room temperature conditions.

 

[snorkack]

It cannot be recovered by any process which returns both the system and surrounding to their original state, unless the original process is reversible. This is a consequence of the 2nd law of thermodynamics.

You cannot recover all of it, by Carnot laws of entropy. When the heat spent on friction raises the temperature of air only slightly above the original/ambient temperature, only a small fraction of frictional energy can be recovered. However, when the heat is spent on friction at temperatures far above the ambient, most of it is recoverable.

The NO concentration within atmospheric air is tiny, and insignificant to the energy balance for the air. See

Look at this part: a common problem with engines is "incomplete combustion" - a lot of chemical energy is left stored in compounds which are also unpleasant to inhale as exhaust gases but which are unreactive enough that combustion is frozen out as the exhaust gases cool on expanding to power the engine.
Engines of infernal combustion sometimes have catalysts on the exhaust. These catalyse exothermal reactions of the exhaust gases that are too unreactive to react spontaneously at these temperatures. Catalysts on engine exhaust produce significant amounts of heat.
Unpleasant gases in engine exhaust which react with help of catalysts but pass into exhaust in absence of catalyst include NO.
How much heat in engine catalysts is produced by the catalysed reaction
2NO=N₂+O₂?
Now suppose that you run an engine but do not actually supply any fuel. Like the shaft of an infernal combustion engine is turned by a starter engine but the benzine tank is empty. Or a turbine engine is freely windmilling but the fuel tank is empty or the tap shut.
How much mechanical energy is lost to drag by engine running with no fuel?
As air is compressed in piston and then expands, most mechanic energy is recovered as from a spring - but while the air is heated by adiabatic compression, a little heat will diffuse into the metal. How do you calculate the amount? Ditto with a turbine engine.
Would an infernal combustion engine or a turbine engine running empty also spend energy to convert air into nitrogen monoxide during the flash compressional heating?

 

[Ax_xiom]

The OP strongly implied air at conditions not grossly removed from typical room temperature conditions

Yes but as far as I know, "typical room temperature conditions" and "880 million tsar bombas worth of energy in as much air as a large coke bottle" can't really coexist. That's why I said that the model likely breaks down as (as far as I know) CFD models are built for air and whatever that becomes after taking that much energy is not going to be air.

 

[Chestermiller]

Yes but as far as I know, "typical room temperature conditions" and "880 million tsar bombas worth of energy in as much air as a large coke bottle" can't really coexist. That's why I said that the model likely breaks down as (as far as I know) CFD models are built for air and whatever that becomes after taking that much energy is not going to be air.

Oops. I didn't really notice the large quantities of energy the OP was referring to.

 

[Ax_xiom]

Oops. I didn't really notice the large quantities of energy the OP was referring to.

Actually quick question, what causes energy losses in adiabatic compression? If heat is being radiated outwards wouldn't that cause the compression to not be adiabatic anymore?

 

[jbriggs444]

Actually quick question, what causes energy losses in adiabatic compression? If heat is being radiated outwards wouldn't that cause the compression to not be adiabatic anymore?

If thermal energy is conducted (or radiated) away during the cycle then yes, it is no longer a perfectly adiabatic cycle.

It can still be mostly adiabatic. We could usefully model it as an adiabatic cycle plus some thermal energy loss. We might add in friction and consider mechanical energy loss as well.