Pressure: Question 8

Worked solution

Part (a): What supports the mercury column

Atmospheric pressure acts on the open surface of the mercury in the dish and pushes mercury up into the tube. At the top of the tube there is a vacuum, which exerts essentially no pressure pushing back down. The mercury rises until the pressure due to the weight of the column exactly balances the atmospheric pressure pushing up from below. At that point the column is supported and stops rising.

Part (b): Why the vertical height stays the same when tilted

The pressure produced at the base of a liquid column depends only on the vertical height of the liquid above that point (not on the length of the path the liquid takes to get there. Since the mercury column still has to balance the same atmospheric pressure as before, its vertical height must still be $760\text{ mm}$. When the tube is tilted, the tube itself becomes longer relative to the vertical, so more mercury is needed to fill it up to that same vertical height) the column inside the tube gets longer, but its vertical height (and therefore the pressure reading) is unchanged.

Part (c): Why mercury rather than water

The height of liquid needed to balance a given atmospheric pressure depends on the liquid’s density: a denser liquid needs a shorter column to produce the same pressure. Mercury has a density of about $13\,600\text{ kg/m}^3$, roughly $13.6$ times the density of water ($1000\text{ kg/m}^3$). Because water is so much less dense, a water barometer would need a column about $13.6 \times 760\text{ mm} \approx 10\,300\text{ mm}$ (over $10\text{ m}$) tall to balance atmospheric pressure, impractically long for a laboratory instrument. Mercury’s high density keeps the column short enough (under a metre) to be practical.

Part (d): Effect of an air leak

A true vacuum at the top of the tube exerts no pressure, so the full weight of the $760\text{ mm}$ mercury column is needed to balance atmospheric pressure. If air leaks into this space, it now exerts a small pressure of its own, pushing down on top of the mercury in addition to the mercury’s own weight. Less mercury height is then needed to balance atmospheric pressure, so the column falls. The barometer gives a reading lower than the true atmospheric pressure (it under-reads).

Final answers

• (a) The column is supported by atmospheric pressure acting on the mercury in the dish, balanced against the vacuum above the column
• (b) Only the vertical height of the column determines the pressure, so it stays at $760\text{ mm}$ even when the tube is tilted
• (c) Mercury’s much higher density means only a short, practical column height is needed, whereas water would need a column about 13.6 times taller (around $10\text{ m}$)
• (d) The mercury height decreases, because the leaked air now exerts its own pressure at the top, so the barometer under-reads atmospheric pressure