# Consider two barometers, one using mercury and another using an unknown liquid. Suppose that the pressure above the liquid in each tube is negligible. The height of the unknown liquid is 13.4 times...

Consider two barometers, one using mercury and another using an unknown liquid. Suppose that the pressure above the liquid in each tube is negligible. The height of the unknown liquid is 13.4 times greater than the height of the mercury. What is the density of the unknown liquid?

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Hello!

A barometer is used for measuring pressure, in our case the atmospheric pressure. This is achieved by balancing atmospheric pressure with the pressure of a liquid column.

The pressure of a liquid column depends only on its height, `P = rho g H,` where `rho` is the density of a liquid, `H` is the height of a column and `g` is the gravity acceleration. Mercury is often used for this purpose because of its high density (about `13.7 (g)/(cm^3)`) which results in a relatively low height.

The `13.4` times greater height of an unknown liquid means that its density is `13.4` times less than that of mercury. It is about `13.7/13.4 approx 1.022 g/(cm^3).` This isn't the density of pure water but close to it; sea water has approximately such a density.