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What is the relationship between pressure and the energy density? I note that the units for pressure (force/area) are the same as (energy/vol) but I am curious to know why this is. Thanks.
Probably none,
the same way moment [n-m] and energy [n-m] have the same units but nothing to do with each other.
uhhh, a radian is a natural unit of twist. as natural as and entire rotation ( radians). twist a shaft with some known torque (nt-m) by one radian. how much energy did it take to do that?
Analytical Dynamics said:The dimensions of work, kinetic energy, and potential energy is a force times a distance. In the US customary system the commonly used unit is the ft-lb. Do not confuse the unit of energy with the unit of a moment, which has the same dimension as energy.
I'd agree with cyrus' when he said, "probably none". What's the definition of "energy density" as it relates to pressure? Is it the energy that is released assuming an isentropic expansion to 0 psia? That might make the most convenient answer, but it really is a miserable definition because that's just the conversion of internal energy to work and there's still plenty of internal energy left after the pressure reaches 0 psia! The fluid may be in liquid or even solid form upon expansion but the temperature is not likely to be anywhere close to absolute zero. There's still energy left. How much? How does the energy relate to pressure? I think I forgot the question already...What is the relationship between pressure and the energy density? I note that the units for pressure (force/area) are the same as (energy/vol) but I am curious to know why this is. Thanks.
I'm afraid the question makes no sense. Regarding rbj's post, those equations may all be well and good, I'm not saying s/he's made a mistake, but those equations don't correlate to the concept of pressure and "energy density". If you want to define energy density in some way and pressure energy in some way, then there might be a correlation, but without some more useful definition there is none.
Note that:
[tex] \frac{U}{m} = C_v \ T = \frac{C_v}{\rho \hat{R}} P [/tex]
reduces to:
[tex] \frac{U}{m} = 1 \ T = \frac{1}{\rho \hat{R}} P [/tex]
This reduces to the ideal gas equation.
I'd agree with cyrus' when he said, "probably none". What's the definition of "energy density" as it relates to pressure? Is it the energy that is released assuming an isentropic expansion to 0 psia? That might make the most convenient answer, but it really is a miserable definition because that's just the conversion of internal energy to work and there's still plenty of internal energy left after the pressure reaches 0 psia! The fluid may be in liquid or even solid form upon expansion but the temperature is not likely to be anywhere close to absolute zero. There's still energy left. How much? How does the energy relate to pressure? I think I forgot the question already...
I'm afraid the question makes no sense. Regarding rbj's post, those equations may all be well and good, I'm not saying s/he's made a mistake, but those equations don't correlate to the concept of pressure and "energy density". If you want to define energy density in some way and pressure energy in some way, then there might be a correlation, but without some more usefull definition there is none.
Note that:
[tex] \frac{U}{m} = C_v \ T = \frac{C_v}{\rho \hat{R}} P [/tex]
reduces to:
[tex] \frac{U}{m} = 1 \ T = \frac{1}{\rho \hat{R}} P [/tex]
This reduces to the ideal gas equation.
i fixed that. my mistake."What's the definition of "energy density" as it relates to pressure? " I'm confused. energy density means the energy contained in a volume. Not U/m, as was suggested.
pV=nRT, right? Note that the units of nRT are joules. Thus
p = joules/vol. = energy density. Doesn't this make sense?
I'd agree 100% that there can be an equation just as you've found, that might somehow give energy per unit volume as a function of pressure in the thermodynamic sense.rbj wrote: does the energy density of a something (a fluid, perhaps, what else can we be talking about regarding pressure and energy density?) have anything to do with the pressure of the something?
i think, for the case that the something is an ideal gas, the answer is "yes".