How do I calculate the gravitational mass of a cylinder of compressed gas, including the effects of pressure? By gravitational mass, I mean what I would measure on an ideal mass balance.(adsbygoogle = window.adsbygoogle || []).push({});

(I know that the pressure is negligibly small in a realistic container, but I want to have a conceptual understanding.)

My understanding is that the time time component of the Ricci curvature is $$R_{00}=\frac{1}{2}\left(\rho_E+P_x+P_y+P_z\right)$$

so pressure should have an analogous contribution to energy on gravity. But I've never seen it applied to any sort of ordinary objects so I'm having a hard time connecting it to reality.

Suppose the gas has a energy of ##E_g##, a pressure of ##P##, and a volume ##V##. The cylinder has an energy ##E_c## and a wall tension of ##-P## due to the confinement of the gas and a surface area ##A##.

If we ignore pressure, then the gravitational mass is just ##(E_g+E_c)/c^2##.

Is the pressure contribution then just ##3PV/c^2##? So the total gravitational mass is ##(E_g+E_c+3PV)/c^2##?

Is the wall tension irrelevant because the wall has 0 volume?

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# I Gravity due to pressure

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