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Chapter 11: Problem 4

A mercury barometer develops a leak, allowing some air to enter the glass tube. Will such a barometer read too high or too low a pressure? Explain your answer.

Short Answer

Expert verified
A leaky mercury barometer will read too low a pressure. This is because the air entering the glass tube creates additional pressure inside the tube, opposing the atmospheric pressure and causing the mercury column to drop. Consequently, the pressure reading will be lower than the actual atmospheric pressure.

Step by step solution

01

Understand the working principle of a mercury barometer

A mercury barometer is an instrument used to measure atmospheric pressure. It consists of a glass tube filled with mercury, which is then inverted and submerged into a reservoir of mercury. Normally, the upper portion of the tube has a vacuum, which ensures that the only force acting on the mercury column is the atmospheric pressure. The height of the mercury column in the tube directly relates to the atmospheric pressure.
02

Analyze the effect of air entering the glass tube

When a leak occurs in the mercury barometer, air enters the glass tube. This creates an additional pressure inside the tube that directly opposes the atmospheric pressure acting on the mercury column. Since the force of the leaky air inside the tube is upward, it will cause the mercury column to drop.
03

Determine the change in the pressure reading

As a consequence of the air entering the tube and opposing the atmospheric pressure, the mercury column will be lower than it would be without the leak. Therefore, the pressure reading obtained from such a barometer will be lower than the actual atmospheric pressure due to the presence of air in the tube.
04

Conclusion

A mercury barometer with a leak that allows air to enter the glass tube will read a lower pressure than the actual atmospheric pressure. This is because the additional air pressure inside the tube acts against the atmospheric pressure, causing the mercury column to drop. Thus, a leaky mercury barometer will read too low a pressure.

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