How much energy can be stored by compressing a gas to a given pressure?

[RonL]

I wonder if anyone can see a closeness to Maxwell's thought experiment ?
If the compressor is equal to the Demon function and the receiver transmits energy back to the compressor, the force of gravity is an added component not considered by Maxwell's thought experiment.
Just a thought.

 

[Stanley514]

Why we can store much more energy in compressed gas than in compressed spring? Is it because gas is more compressible than spring?
What relation exist between matter deformability and energy storage?

 

[Philip Wood]

Again I re-iterate (from post 4) that you're not storing energy in compressed air unless your method of storage involves raising the temperature of the air (and then, to use the energy, letting it cool again).

But, moving on, what does it mean to say that more energy is stored is stored in a gas than a spring? How much gas are you comparing with how much spring? Please note, I'm not trying to nitpick. I genuinely don't know how one would make a quantitative comparison.

 

[Stanley514]

Again I re-iterate (from post 4) that you're not storing energy in compressed air unless your method of storage involves raising the temperature of the air (and then, to use the energy, letting it cool again).

But, moving on, what does it mean to say that more energy is stored is stored in a gas than a spring? How much gas are you comparing with how much spring? Please note, I'm not trying to nitpick. I genuinely don't know how one would make a quantitative comparison.

It really depend on spring.

Carbon nanotube springs

are springs made of carbon nanotubes (CNTs). They are an alternate form of high density, lightweight, reversible energy storage based on the elastic deformations of CNTs. Many previous studies on the mechanical properties of CNTs have revealed that they possesses high stiffness, strength and flexibility. The Young's modulus of CNTs is 1 TPa and they have the ability to sustain reversible tensile strains of 6%[1] and the mechanical springs based on these structures are likely to surpass the current energy storage capabilities of existing steel springs and provide a viable alternative to electrochemical batteries. The obtainable energy density is predicted to be highest under tensile loading, with an energy density in the springs themselves about 2500 times greater than the energy density that can be reached in steel springs, and 10 times greater than the energy density of lithium-ion batteries..

http://en.wikipedia.org/wiki/Carbon_nanotube_springs
So, why carbon nanotube springs have better energy density than steel springs?

 

[RonL]

Why we can store much more energy in compressed gas than in compressed spring? Is it because gas is more compressible than spring?
What relation exist between matter deformability and energy storage?

You will find weight might be the biggest factor in why either would be considered for a particular function.

 

[Philip Wood]

So, why carbon nanotube springs have better energy density than steel springs?

The energy stored due to tensile stress per unit volume of solid is $u = \frac{1}{2}Y \epsilon^2$ in which Y is the Young modulus and $\epsilon$ is the strain.

Both factors, Y and maximum possible elastic $\epsilon$ are different for the two materials. The carbon-carbon covalent bonds exert more force per unit increase in separation of the atoms than the metallically bonded atoms in steel, leading to the nanotubes having a greater Young modulus than steel. Also, much larger strains can be suffered by the nanotubes than by steel before the material ceases to deform elastically. This is because the metallic bonding (pooled electrons) in the steel allows planes of atoms in crystals to slip over each other (promoted by the presence of dislocations) under moderate stress. This can't happen in the covalently bonded nanotubes, though they do break eventually under VERY large stress.