760 mm. (1 atmo.). Since this pressure is that of a column of mercury 76 cm. high and of 1 sq. cm. section = 76 X 13'6 grams, then in absolute measurement :
1 atmo. = 76 X 13-6 X 981 = 1014 x 10* dynes per sq. cm.
According to Avogadro's hypothesis (see below), a gram- molecule of a gas at 0° and 1 atmo. pressure occupies the volume 22,400 c.c. ; and since, according to Gay-Lussac's (Charles's) law, the volume of a gas (at constant pressure) is proportional to its absolute temperature, the volume of a gram-molecule of water vapour (or any other gas) at 100° is —
V = -^^y X 373 = 82 X 373 c.c.
and at any other temperature T (in absolute degrees)
vr = 82 Tec.
The work, therefore, which has to be done to bring a gram-molecule into the gaseous state is —
Pdv = 1-014 X 82 X W X rergs = 832 megergs.^
We have already seen that 1 cal. =41*8 megergs, con- sequently the work done on vaporising a gram-molecule, expressed in calories, is given by —
OQ.O
A = ?f^r cal. = 2T cal. (or more exactly 1997 cal.).
The external work, therefore, which is done on evolving a gram-molecule of a gas is, when expressed in calories, twice the absolute temperature. The work done on forming a gram-molecule of steam at 100^ is equivalent to 2 x 373 = 74r> calories.
This work is independent of the value of the external pressure. For if the pressure in the preceding example be 2 atmos. instead of one, then, according to Boyle's law, the
^ The syllable meg- before a unit of measurement signifies a million. Thus 1 megerg = 1 million ergs, 1 megohm = 1 million ohms. The
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prefix micro- denotes a millionth; thus, 1 microvolt = 10" volt.
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