- #1

- 495

- 2

On wiki, regarding specific gravity, it gives the derivation for the pycnometer equation for determining specific gravity. However, the first equation confuses me. It goes as follows:

The pycnometer, placed on a balance, will exert a force:

[tex]F = g(m_b - \frac{ \rho_a m_b}{ \rho_b})[/tex]

The subscript b is for the bottle, and a is for air. rho is density and m is mass; g is the acceleration due to gravity

The force on the balance would be F = gm. The above equation suggests that the mass of the air displaced by the bottle needs to be subtracted from the mass of the bottle; so the mass used in the equation is the difference in mass between the bottle and the air that would occupy the space of the material used for the bottle. I don't understand why this is the case. Why does the mass of air that would occupy that space if the bottle wasn't there even matter? It seems irrelevant. Surely we need to consider the mass of the bottle, all of its mass.

Any help appreciated.