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Why is the atmospheric pressure given as the value of length of mercury column in barometer. Since the density for the both the cases are different.

Is it that by experiment we found the value to be same or it has some scientific relation with mercury and atmosphere

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Since the density for the both the cases are different.

The density of mercury will remain the same. The density of the air will vary with pressure and that's exactly what you want to measure.

The air pressure pushes the mercury up the tube and, since the top of the tube is a vacuum, there is no counter-pressure.

  • Mercury has a density of 13.6 g/cm3.
  • 1 atmosphere pressure (1 bar) = 1029.7 g/cm2.

Now how tall (h) a column of mercury can 1 bar support? (Rough figures below.)

$$ h = \frac {pressure}{density} = \frac {1030}{13.6} = 75.7 \ \text {cm} $$

As air pressure goes up and down the height of the column of mercury will rise and fall in proportion.

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  • $\begingroup$ Deleting my comments, cheers. And certain values are "fixed" in my head from using them so often - just like you have your "set" :) $\endgroup$
    – Solar Mike
    Jan 23 at 16:47
  • $\begingroup$ Is it like when the mercury goes into the barometer, at that time , air is pushing it inside. Now as it fills to a height 76cm , then it the time when air pressure can’t force it more up and mercury pressure can take the load of air pressure which is coming from down.? Therefore acceleration = 0. So they are both equal. $\endgroup$
    – srijan Sri
    Jan 23 at 17:08
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    $\begingroup$ Yes. The pressure of the air is balanced by the weight of the mercury. When you are at sea level there is > 1 kg of air pressure on every square cm of your skin! Of course the pressure inside your body is the same so you don't collapse. $\endgroup$
    – Transistor
    Jan 23 at 17:11
  • $\begingroup$ @Transistor amazing . Thank you so much . $\endgroup$
    – srijan Sri
    Jan 23 at 17:16
  • $\begingroup$ @Transistor I want to ask about the derivation of pseudo force. Which is the right tag I should use ? $\endgroup$
    – srijan Sri
    Jan 23 at 17:19
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Most labs have a mercury barometer in them to give the atmospheric pressure.

Usually taken at the start and end of a test - especially when dealing with engines, also ambient temperature and humidity are taken as well.

The "lab standard" mercury barometers also have a temperature correction chart to correct the indicated reading due to the temperature variation of ambient from the barometer calibrated standard.

The reading is usually in mmHg and then this can be converted into pascals or other units as needed, but most of us know the source of the mmHg reading and expect it to be within a given range.

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  • $\begingroup$ Perfect. One more thing , I wanted to ask about derivation of pseudo force. Can you tell me the right tag for it ? $\endgroup$
    – srijan Sri
    Jan 23 at 17:24
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Because of the fear of being accused of witchcraft, of all things.

The mercury barometer is the oldest type of barometer, invented by the Italian physicist Evangelista Torricelli in 1643. Torricelli conducted his first barometric experiments using a tube of water. Water is relatively light in weight, so a very tall tube with a large amount of water had to be used in order to compensate for the heavier weight of atmospheric pressure.

Torricelli’s water barometer was more than 10 meters (35 feet) in height, which rose above the roof of his home! This odd device caused suspicion among Torricelli’s neighbors, who thought he was involved in witchcraft. In order to keep his experiments more secretive, Torricelli deduced that he could create a much smaller barometer using mercury, a silvery liquid that weighs 14 times as much as water.

https://www.nationalgeographic.org/encyclopedia/barometer/#:~:text=The%20mercury%20barometer%20is%20the,using%20a%20tube%20of%20water.

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