Question

A mercury barometer with a tube of uniform diameter and length 840mm above the mercury level in the reservoir, reads 740mm on a day when the atmospheric pressure is 760mmHg. Estimate the pressure of the atmosphere on a day when it reads 720mm. Assume the average temperature is the same on both days

Answer 1

Answer on Question #77369, Physics / Other

A mercury barometer with a tube of uniform diameter and length 840 mm above the mercury level in the reservoir, reads 740 mm on a day when the atmospheric pressure is 760 mmHg. Estimate the pressure of the atmosphere on a day when it reads 720 mm. Assume the average temperature is the same on both days.

Solution:

Initially the length of trapped air in the tube

$$l _ {1} = 8 4 0 - 7 4 0 = 1 0 0 m m.$$

Volume of the trapped air

$$V _ {1} = l _ {1} A$$

where A is the area of cross-section of the tube.

Pressure of the trapped air

$$P _ {1} = 7 6 0 - 7 4 0 = 2 0 m m o f H g.$$

On another day, the volume of the trapped air

$$V _ {2} = l _ {2} A$$

where

$$l _ {2} = 8 4 0 - 7 2 0 = 1 2 0 m m$$

Let the pressure of the trapped air be $\mathrm{P}_2\mathrm{mm}$ of Hg.

By Boyle's law,

$$P _ {1} V _ {1} = P _ {2} V _ {2}$$

So,

$$P _ {2} = P _ {1} \frac {V _ {1}}{V _ {2}} = P _ {1} \frac {l _ {1}}{l _ {2}} = 2 0 \times \frac {1 0 0}{1 2 0} = 1 6. 7 m m o f H g.$$

Atmospheric pressure

$$P = 7 2 0 + 1 6. 7 = 7 3 6. 7 m m H g$$

Answer: $736.7 \, \text{mmHg}$ .

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