Posted: Jan 05, 2019 7:59 pm
romansh wrote:A few years back I noticed that (in our meso world) pressure had the same units as energy density.

I think it's customary to define a pascal as a newton per square metre: 1 Pa = 1 N/m2. Pressure is the force exerted on a two-dimensional area: say the force exerted by the air in a balloon on the rubber skin, or the force exerted by the plasma in a star on a shell (centred on the centre of the star) contained within the star's volume.

Certainly you can multiply numerator and denominator by m and get 1 Pa = 1 Nm/m3 = 1J/m3. I was going to go on to say that I was not sure how helpful it is, and ask rhetorically what in the real world corresponds to this volume represented by m3. But on reflection it is interesting to consider that when a gas exerts a force of 1 newton on a square metre of balloon skin or shell contained in a star, this corresponds to 1 joule of energy per cubic metre of the gas.

That is, obviously, not to say that there really is a joule of energy in each cubic metre of the gas: that energy density is only given in the layer of gas that is actually exerting the pascal of pressure on the two-dimensional area, and it may fall off or increase the further away from that area you measure. The energy density seems more likely to be constant throughout the gas in the case of a balloon than a star.

Interesting.