Question

In the middle of a narrow horizontal tube sealed at both ends is a column of mercury 10cm in length. Both halves of the tube contain air under a pressure of 76cm of mercury. By what distance will the mercury column be displaced if the tube is held vertically? The length of the tube is 1 m. 

Answer 1

Answer: x = 2.95cm

Explanation:

We denote by x the displacement of the mercury column, by l₀ the length of tube occupied by the gas in each half of the tube in the horizontal position, by P₁ and P₂ the gas pressure in the upper and lower halves of the tube after being placed in a vertical position, by h₀ the length of the mercury column. The equations of the change of state of the gas in each half of the tube may now be written in the following form:

The solution of this set of equations gives the result we are seeking.