If a barometer was filled with milk (density =1.02 g/ml) rather than mercury, how tall would the barometer have to be to contain this solution?

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justaguide eNotes educator| Certified Educator

The barometer is filled with milk instead of mercury. It is assumed that the ambient temperature is 20 C and the barometer is at sea level. The density of milk is 1.02 g/ml, the density of mercury is 13.59 g/ml.

The average air pressure at sea level is 101.325 kPa or 760 mm of Hg. If a barometer were filled with mercury and placed at sea level, the pressure of air would be able to support a column of mercury 760 mm high. As the density of milk is lower than that of mercury, the height of a column of milk that can be supported at the same pressure is going to be higher.

As the density of mercury is 13.59/1.02 = 13.32 times that of milk, the appropriate height of a barometer filled with milk would have to be 760*13.32 = 101.25 cm.

You need a barometer that is 101.25 cm tall to be able to measure atmospheric pressure at sea level using milk instead of mercury.

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