Atmospheric pressure

Atmospheric pressure, Torricelli's experiment, the barometer, normal atmospheric pressure of $760$ mm Hg, how the pressure changes with height.

Terms

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Formulas

Pressure of a mercury column (Torricelli's experiment)

p_{\text{атм}} = \rho_{\text{рт}}\, g\, h

Quantities
Symbol	Name	Unit
$p_{\text{атм}}$	atmospheric pressure (pressure of the mercury column)	Pa
$\rho_{\text{рт}}$	density of mercury, $13\,600$	kg/m³
$g$	acceleration due to gravity	m/s²
$h$	height of the mercury column in the tube	m

Solved for another quantity:

h = \dfrac{p_{\text{атм}}}{\rho_{\text{рт}}\, g}

p = 133{,}3 \cdot h_{\mathrm{mm}}

Note. Example ( $g = 9.8\ \text{m/s}^2$ ): $h = 0.76\ \text{m}$ , $p = 13\,600 \cdot 9.8 \cdot 0.76 \approx 101\,300\ \text{Pa}$ . Convert the height of the column to metres. With $g = 10\ \text{m/s}^2$ you get $103\,360\ \text{Pa}$ , a little more than the table value, so in problems with mm Hg the conversion $1\ \text{mm Hg} \approx 133.3\ \text{Pa}$ is usually used.

Normal pressure, mm Hg and pascals

760 \cdot 133{,}3 \approx 101\,300

Quantities
Symbol	Name	Unit
$p_{\mathrm{mmHg}}$	pressure in mm Hg	mm Hg
$p$	pressure in pascals	Pa

Solved for another quantity:

p = 133{,}3\, p_{\mathrm{mmHg}}

p_{\mathrm{mmHg}} = \dfrac{p}{133{,}3}

Note. $1\ \text{mm Hg} \approx 133.3\ \text{Pa}$ . Example: $740\ \text{mm Hg} = 740 \cdot 133.3 \approx 98\,600\ \text{Pa}$ ; the other way: $100\,000\ \text{Pa} \approx 750\ \text{mm Hg}$ . The unit is off-system, so it is converted to pascals in calculations. $1\ \text{hPa} = 100\ \text{Pa}$ .

Change of pressure with height (approximate)

\Delta p \approx \dfrac{\Delta H}{12}

Quantities
Symbol	Name	Unit
$\Delta p$	decrease of pressure	mm Hg
$\Delta H$	ascent above the surface	m

Solved for another quantity:

\Delta H \approx 12\,\Delta p

p = p_0 - \dfrac{H}{12}

Note. A textbook rule: going up $12$ m lowers the pressure by $1$ mm Hg. Example: on a roof $60$ m high the pressure is lower by $\dfrac{60}{12} = 5$ mm Hg, so instead of $760$ it is $755$ mm Hg. The rule is approximate and holds for small heights.

Lab

Set the quantities with the sliders. The graphs and the formulas with your numbers update at once.

Torricelli's tube

The pressure of the mercury column balances the atmospheric pressure. The lower the atmospheric pressure, the lower the column. The height of the column in mm equals the pressure in mm Hg.

Graphs

The line p(H) shows how the pressure falls with ascent (qualitatively: 1 mm Hg per 12 m). Click the graph to set the height.

p(H)

H

0 m

p

760 mm Hg ≈ 101,308 Pa

h

760 mm

Formulas with your numbers

p = p_0 - \dfrac{H}{12} = 760 - \dfrac{0}{12} = 760\ \text{mm Hg}

p = \rho g h = 13600\cdot 9.8\cdot 0.76 = 101293\ \text{Pa}

How to read the graphs

The $p(H)$ graph is a falling straight line: the higher above sea level, the lower the atmospheric pressure. The graph is qualitative: it holds near the Earth's surface, for small ascents.
The slope of the line is $1$ mm Hg for every $12$ m of ascent. Going up $120$ m lowers the pressure by $10$ mm Hg, for example from $760$ to $750$ mm Hg.
The slider for the pressure at the surface moves the line up or down while the slope stays the same: the pressure changes, but the rule of « $12$ m per $1$ mm Hg» does not.
The height of the mercury column in Torricelli's tube (in millimetres) equals the pressure in mm Hg. So as you go up, the column in the tube gets lower.

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Terms

Studied 0 of 5

Formulas

Pressure of a mercury column (Torricelli's experiment)

p_{\text{атм}} = \rho_{\text{рт}}\, g\, h

Quantities
Symbol	Name	Unit
$p_{\text{атм}}$	atmospheric pressure (pressure of the mercury column)	Pa
$\rho_{\text{рт}}$	density of mercury, $13\,600$	kg/m³
$g$	acceleration due to gravity	m/s²
$h$	height of the mercury column in the tube	m

Solved for another quantity:

h = \dfrac{p_{\text{атм}}}{\rho_{\text{рт}}\, g}

p = 133{,}3 \cdot h_{\mathrm{mm}}

Normal pressure, mm Hg and pascals

760 \cdot 133{,}3 \approx 101\,300

Quantities
Symbol	Name	Unit
$p_{\mathrm{mmHg}}$	pressure in mm Hg	mm Hg
$p$	pressure in pascals	Pa

Solved for another quantity:

p = 133{,}3\, p_{\mathrm{mmHg}}

p_{\mathrm{mmHg}} = \dfrac{p}{133{,}3}

Change of pressure with height (approximate)

\Delta p \approx \dfrac{\Delta H}{12}

Quantities
Symbol	Name	Unit
$\Delta p$	decrease of pressure	mm Hg
$\Delta H$	ascent above the surface	m

Solved for another quantity:

\Delta H \approx 12\,\Delta p

p = p_0 - \dfrac{H}{12}

Lab

Set the quantities with the sliders. The graphs and the formulas with your numbers update at once.

Torricelli's tube

The pressure of the mercury column balances the atmospheric pressure. The lower the atmospheric pressure, the lower the column. The height of the column in mm equals the pressure in mm Hg.

Graphs

The line p(H) shows how the pressure falls with ascent (qualitatively: 1 mm Hg per 12 m). Click the graph to set the height.

p(H)

H

0 m

p

760 mm Hg ≈ 101,308 Pa

h

760 mm

Formulas with your numbers

p = p_0 - \dfrac{H}{12} = 760 - \dfrac{0}{12} = 760\ \text{mm Hg}

p = \rho g h = 13600\cdot 9.8\cdot 0.76 = 101293\ \text{Pa}

How to read the graphs

The

p(H)

graph is a falling straight line: the higher above sea level, the lower the atmospheric pressure. The graph is qualitative: it holds near the Earth's surface, for small ascents.

The slope of the line is

1

mm Hg for every

12

m of ascent. Going up

120

m lowers the pressure by

10

mm Hg, for example from

760

750

mm Hg.

The slider for the pressure at the surface moves the line up or down while the slope stays the same: the pressure changes, but the rule of «

12

m per

1

mm Hg» does not.

The height of the mercury column in Torricelli's tube (in millimetres) equals the pressure in mm Hg. So as you go up, the column in the tube gets lower.