Physics
Physics
Problem
A column of mercury of length 10 cm is contained in the middle of a horizontal tube of length 1 m which is closed at both the ends. The two equal lengths contain air at standard atmospheric pressure of of mercury. The tube is now turned to vertical position. By what distance (in cm) will the column of mercury be displaced? (Assume temperature to be constant) ?Intuitive explanation
When a horizontal tube flips vertical, the mercury column's weight now creates an additional pressure difference between the air above and below it. The key is to use Boyle's Law on each air column separately—as mercury shifts, one air column compresses while the other expands, and their pressure changes must balance the mercury's weight. Set up pressure equations for the new equilibrium: the pressure difference across the mercury equals (its weight per unit area), then solve for the displacement using the constraint that for each trapped air pocket.
Intuitive explanation
When a horizontal tube flips vertical, the mercury column's weight now creates an additional pressure difference between the air above and below it. The key is to use Boyle's Law on each air column separately—as mercury shifts, one air column compresses while the other expands, and their pressure changes must balance the mercury's weight. Set up pressure equations for the new equilibrium: the pressure difference across the mercury equals (its weight per unit area), then solve for the displacement using the constraint that for each trapped air pocket.