9. Mass Density (ρ, Greek “rho”) = Mass/Volume
For example, ρwater = 1.0 gm/cm3
ρair = 1.3 x 10-3 gm/cm3 (varies with T and p)
= 1.3 kg/m3
ρMercury= 13.6 gm/cm3

10. Mass density, ρ ρ = number x molecular per volume mass ρ = n x m
Near sea level, nair = 2.72 x cm-3
and mair = 4.81 x gm
so ρair = 1.3 x 10-3 gm/cm3
NOTE: ρair depends on pressure (or altitude) and the
air temperature.

11. Gas Law p = n k T where n = number density (or number/volume)
What is connection between the pressure of a gas and temperature?
Gas Law p = n k T
where n = number density (or number/volume)
and k = Boltzmann’s constant
= 1.38 x °K (cgs units)
= 1.38 x °K (mks units)
and the temperature, T, is in degrees Kelvin
Basically, p = (Number/Volume) x Temperature or
p x V = (Constant) x T

12. Sketches by C. Weidman

15. Units of pressure Pressure = Force/Area
p = (Mass x Acceleration) /Area
p = (Mass x gravity)/Area
p = Mass/Area x gravity
p = (M/A) x g
Pressure = (Mass of liquid/Area) x g
where g = acceleration of gravity

16. Units of pressure - 2
Now, consider a water barometer with a 1 cm2 cross-sectional area
Many experiments near sea level show that the average height, H, of a water barometer is about meters or 1033 cm.
Water has a mass density of 1.0 gm per cm3.
Therefore, the total mass of water in a 1033 m column (above an area of 1 cm2) is
Volume = Area x Height
V = 1 cm2 x 1033 cm
V = 1033 cm3 (per cm2)
Now, since the density of water is 1 gm per cm3, the total mass above a 1 cm2 area is
Mass per cm2 = Density x Volume (per cm2)
M/A = 1 gm/cm3 x 1033 cm3 (per cm2)
M/A = 1033 gm/cm2

17. Units of pressure - 3
Now, since the average acceleration of gravity at sea level is
g = m/sec2 = cm/sec2,
we can multiply the mass (per cm2) by g to get the force per area
(or pressure) in physical units
p = M/A x g
= 1033 gm/cm2 x cm/sec2
= x 106 gm cm/sec2 per cm2 or
= x 106 dynes per cm2
DEFINITION: bar ≡ 106 dynes/cm2
which makes p = bars = 1013 x 10-3 bars
or p = 1013 millibars (mb)
near sea level.

18. Units of pressure - 4
In the meter-kilogram-sec (or mks) system of units,
p = M/A x g
= 1033 gm/cm2 x 10-3 kg/gm x 104 cm2/m2 x 9.8 m/sec2
p = x 105 kg m/sec2/m2
p = x 105 Nt/m2
p = x 105 Pascals (Pa)
Note: 1 mb = 10-3 bars = 100 Pa = 1 hectoPascals (hPa)

19. SUMMARY Units of pressure - 5 One atmosphere, patm = 33.9 feet water
= 10.3 m = 1033 cm water
= 1033 gm/cm2 (atmospheric depth)
= kg/cm2
=1.033 x 104 kg/m2
= 760 mm Mercury (Hg)
= 76 cm Hg
= inches Hg

20. Units of pressure - 6
In cgs units, patm = bars
= 1013 millibars (mb)
where 1 bar = 106 dynes/cm2 and 1 mb = 103 dynes/cm2.

21. Units of pressure - 5
In mks units, patm = x 105 Pascals (Pa)
= kiloPascals (kPa)
= 1013 hectoPascals (hPa)
Note: 1 mb = 1 hPa

22. Average
Sea Level
Pressure
June
July
August
December
January
February

23. Rawinsonde measures pressure, temperature, dew point, wind speed, and wind direction as function of altitude. Every 12 hours, worldwide at 00:00 and 12:00 GMT

28. Air pressure decreases rapidly (exponentially) with altitude.

30. Graph of balloon measurements of the upper atmosphere
Temperature (red)
Dew Point (blue)
(both in ºC)