Generalisation of Torr's experiment

[Backes]

Hey, I bet that many of you know Torr, or mm/hg. It is defined as 1/760 of the standard atmospheric pressure. Below is an image of the setup to determine the value. My idea was to simply look for a formula to calculate the height for any fluid, not only Hg.

 

It sounds not that hard, and is in fact pretty easy, BUT... My results are somehow not accurate.

[latex]P_{ext}= P_{int}
\Leftrightarrow P_{ext} = \frac{m \times g}{\pi \times r^2}
\Leftrightarrow P_{ext} = \frac{\rho \times h \times \pi \times r^2 \times g}{\pi \times r^2}
\Leftrightarrow P_{ext} = \rho \times h \times g
\Leftrightarrow h = \frac{P_{ext}}{\rho \times g}[/latex]

(please ingore the <br>, linebreaks are somehow interpreted wrong... I did not post them )

With [latex]\rho[/latex] the density of the fluid.

When I know take those values: g = 9.81 N/kg and the density as 13.534 g/cm^3 (wikipedia) at 20°C and as outside pressure 1atm, which is 1013.25 hPA I get as a result 763,17mm. Did I miss something in the calculation? I don't think so... So where did I took a "wrong" value? Do I need to take the density of Hg at 0°C? Or is my g not accurate?

 

Thank you!

[swansont]

Density is temperature-dependent, and g is also not fixed. 15.534 13.534g/cm³ "near room temperature", but the page on torr uses 13.5951 g/cm³ (and also 9.80665 m/s² for g); a standard atmosphere is indeed defined at 0ºC rather than room temperature, so your guesses were right.

[John Cuthber]

Density is temperature-dependent, and g is also not fixed. 15.534 g/cm³ "near room temperature", but the page on torr uses 13.5951 g/cm³ (and also 9.80665 m/s² for g); a standard atmosphere is indeed defined at 0ºC rather than room temperature, so your guesses were right.

Oops! typo

13.534 rather than 15.534