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I've seem sometimes the atmosphere unit for pressure be defined so that $1\ \mathrm{atm}$ would be the mean atmospheric pressure at sea level.

I've seem on the other hand the following definition:

One standard atmosphere is the pressure produced by a column of mercury exactly $76\ \mathrm{cm}$ high, at a temperature of $0^\circ\mathrm{C}$, and at a point where $g = 980.665 \ \mathrm{cm}\ \mathrm{s^{-2}}$.

Perhaps the need to specify the temperature and gravity acceleration are obvious to people more acquainted with experimental physics, but I know nothing of this stuff and so for me I don't get why people would define it like that.

This is IMHO one experimental definition, because it is saying how can one go there in practice and measure $1 \ \mathrm{atm}$. But temperature and gravity acceleration doesn't seem at first to come into play here.

Why does one need to specify the temperature and gravity acceleration when making this definition?

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  • $\begingroup$ It was defined like that because there were a lot of mercury pressure meters and barometers around. The local gravity is tabulated and the temperature can be measured reasonably well, so the actual measurements can be corrected for. We have replaced our mercury based equipment with less toxic equipment and standard atmospheres have been replaced with SI units of $1 Pascal = 1 N/m^2$ and $1 bar = 10^5 Pascal$. $\endgroup$
    – CuriousOne
    Commented Mar 14, 2016 at 3:55

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Why does one need to specify the temperature and gravity acceleration when making this definition?

"Centimeters of mercury" (as measured by a mercury barometer) is not the best measure of atmospheric pressure. In addition to being sensitive to atmospheric pressure, a mercury barometer is sensitive to temperature of the mercury and the local strength of gravitational acceleration.

The column of mercury is presumably in hydrostatic equilibrium. In this case, the change in pressure due to changes in height is given by$$\frac{dP}{dh} = -\rho g$$ Assuming a constant density and constant gravitational acceleration throughout the mercury means that the height of the column is $$h = \frac{P_a}{\rho g}$$ The height of the column depends not only on atmospheric pressure but also on density and local gravitational acceleration. So why the dependence on temperature? The latter comes into play because the density of mercury varies with temperature.

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Why does one need to specify the temperature and gravity acceleration when making this definition?>

The mercury barometer (pressure measuring instrument) uses a column of mercury dipped in a container of Hg -which is supported by the atmospheric pressure; so its equal to ( h.density of mercury.g ); where h is height of the column.

Therefore the local value of g must be quoted with the standard value and the density of mercury taken as at standard temperature 0 degree centigrade.

The standard was defined perhaps at Paris , thereby the local g -value has been quoted. we still use a mercury based Barometer called Fortin's Barometer in our Laboratories. The standard atmosphere presure is equivalent to 1.01325 bar or 760 torr or 101325 Pa.

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