A small amount of air is introduced into the vacuum above the mercury in a mercury barometer tube. The mercury level goes down because the air molecules

Analyzing the question

A mercury barometer works by balancing atmospheric pressure against the weight of a mercury column. Above the mercury in the tube is a vacuum (the Torricelli vacuum), which exerts no pressure. The question asks why the mercury level falls when a little air gets into this space.

The concept

• Atmospheric pressure pushes on the mercury in the dish and supports the column in the tube.
• At equilibrium: Atmospheric pressure = pressure of the mercury column + pressure of any gas above the mercury.
• In a perfect barometer, the pressure above the mercury is zero, so the column height (about 760 mmHg) gives the full atmospheric pressure.

Step-by-step solution

1. Air molecules enter the vacuum space above the mercury.
2. These molecules move randomly and collide with the mercury surface and the tube walls. This creates a pressure in the space above the mercury.
3. This extra pressure pushes down on the mercury column.
4. Atmospheric pressure must now balance both the mercury column and the trapped air pressure: P_atm = P_air + hρg
5. Since P_atm stays constant, hρg must decrease, so the mercury height h drops.

Evaluating the options

• A. Heating and expansion would make the level rise, and air molecules don't heat the mercury significantly. ✗
• B. The pressure above the mercury increases, which pushes the level down. ✓
• C. Cooling and contraction is not the cause. ✗
• D. A decrease in pressure above the mercury would make the level rise, not fall. ✗

Answer: B

Exam tip: Remember that in a barometer, the height of the column is inversely related to the pressure above it. More gas above the mercury means a lower column, which is why a faulty barometer reads too low. Always ask yourself: "What is pushing down, and what is pushing up?"