Use mercury barometer to fing height of building

In summary, the conversation discusses using a mercury barometer to determine the height of a building. The setup involves finding the difference in pressures for mercury and using its density to calculate the pressure. However, there may be an error as the given density for mercury is 10 times greater than its actual value.
  • #1
stuplato
34
0
A mercury barometer reads 700.0 mm on the roof of a building and 715 mm on the ground. Assuming a constant value of 1.29 kg/m3 for the density of air, determine the height of the building.
.
My setup was finding the difference in the pressures for mercury and get 15 mm Hg
Then use Hg density = 136000 to get a pressure using P=pgh
So P will equal 1999200
then subtract atmosphere pressure and divide the result by 12.642 (pg)
But the answer is wrong... Where did I go astray?
 
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  • #2
I haven't checked anything else, but the specific gravity of mercury is 13.6, so its density is 13.6 times greater than water, so density of mercury is 13.6*10^3 = 13,600 kg/m^3.
You have 10 times that value, 136,000, or that a typo ??
 
  • #3


It seems that you have made a mistake in your calculations. The correct way to use a mercury barometer to find the height of a building is to first find the difference in pressure between the roof and the ground. In this case, the difference is 15 mm Hg. Then, using the density of mercury (13,600 kg/m3), you can calculate the pressure difference in terms of height using the equation P = pgh, where p is the density of mercury, g is the acceleration due to gravity (9.8 m/s2), and h is the height. So, in this case, the pressure difference in terms of height would be (15 mm Hg)(13,600 kg/m3)(9.8 m/s2) = 2,058,000 kg/m2.

Next, you need to convert this pressure into meters by dividing by the density of air (1.29 kg/m3). This gives a height of 1,595.3 meters. However, this is the height of the column of mercury, not the height of the building. To find the height of the building, you need to subtract the height of the mercury column from the total height of the barometer (which is 700 mm on the roof and 715 mm on the ground). This gives a difference of 15 mm, which is the height of the building. So, the height of the building is 15 meters.

In summary, the correct way to use a mercury barometer to find the height of a building is to first find the pressure difference in terms of height, then convert to meters, and finally subtract the height of the mercury column from the total height of the barometer to find the height of the building. It is important to double check your calculations and units to ensure accuracy in your results.
 

1. How does a mercury barometer work?

A mercury barometer works by using the weight of mercury in a sealed tube to measure the atmospheric pressure. As the atmospheric pressure changes, the height of the mercury column in the tube will also change, giving an indication of the pressure.

2. Why is a mercury barometer used to measure the height of a building?

A mercury barometer is used because it is a simple and accurate tool for measuring atmospheric pressure, which can then be used to calculate the height of a building using the equation: height = (atmospheric pressure difference x density of mercury x acceleration due to gravity) / (density of air)

3. Is using a mercury barometer to measure the height of a building safe?

No, it is not safe to use a mercury barometer to measure the height of a building as mercury is a toxic substance. It is important to handle the barometer carefully and dispose of it properly.

4. Can a mercury barometer be used to measure the height of any type of building?

Yes, a mercury barometer can be used to measure the height of any type of building as long as it is able to accurately measure the atmospheric pressure at the base and the top of the building.

5. Are there any limitations to using a mercury barometer to measure the height of a building?

Yes, there are some limitations to using a mercury barometer. It can only measure the height of a building accurately if the atmospheric pressure at the base and the top of the building is consistent and there are no significant changes in the weather conditions. Additionally, the barometer must be properly calibrated for accurate readings.

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