(1) The amount of work necessary to produce a unit of heat by the
compression of a gas is the same for all gases at the same temperature;
(2) And that the quantity of heat evolved in all circumstances, when the
temperature of the gas is given, is proportional to the amount of work
spent in the compression.
51. The expression for the amount of work necessary to produce a unit of
heat is
μ(1 + _Et_)/(_E_),
and therefore Regnault’s experiments on steam are available to enable us
to calculate its value for any temperature. By finding the values of μ
at 0°, 10°, 20°, etc., from Table I., and by substituting successively
the values 0, 10, 20, etc., for _t_, the following results have been
obtained:
TABLE OF THE VALUES OF (μ(1 + _Et_))/(_E_).
───────────────────────────────────┬───────────────────────────────────
Work requisite to produce a unit of│ Temperature of the Gas.
Heat by the compression of a Gas. │
───────────────────────────────────┼───────────────────────────────────
Ft.-pounds. │ °
1357.1 │ 0
1368.7 │ 10
1379.0 │ 20
1388.0 │ 30
1395.7 │ 40
1401.8 │ 50
1406.7 │ 60
1412.0 │ 70
1417.6 │ 80
1424.0 │ 90
1430.6 │ 100
1438.2 │ 110
1446.4 │ 120
1455.8 │ 130
1465.3 │ 140
1475.8 │ 150
1489.2 │ 160
1499.0 │ 170
1511.3 │ 180
1523.5 │ 190
1536.5 │ 200
1550.2 │ 210
1564.0 │ 220
1577.8 │ 230
───────────────────────────────────┴───────────────────────────────────
Mr. Joule’s experiments were all conducted at temperatures from 50° to
about 60° Fahr., or from 10° to 16° Cent.; and consequently, although
some irregular differences in the results, attributable to errors of
observation inseparable from experiments of such a very difficult
nature, are presented, no regular dependence on the temperature is
observable. From three separate series of experiments, Mr. Joule deduces
the following numbers for the work, in foot-pounds, necessary to produce
a thermic unit Fahrenheit by the compression of a gas.
820, 814, 760.
Multiplying these by 1.8, to get the corresponding number for a thermic
unit Centigrade, we
1476, 1465, and 1368.
The largest of these numbers is most nearly conformable with Mr. Joule’s
views of the relation between such experimental “equivalents,” and
others which he obtained in his electro-magnetic researches; but the
smallest agrees almost perfectly with the indications of Carnot’s
theory; from which, as exhibited in the preceding table, we should
expect, from the temperature in Mr. Joule’s experiments, to find a
number between 1369 and 1379 as the result.[62]