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less mass than the warmer one, it gains n times more degrees
than the warmer one loses; f.e. 1 lb. water at 100° and 3 lbs. at
20° make a mixture of 40°. If the 3 lbs. lose x degrees, we get
the following equation:
100 - 3x = 20 + x
100 = 20 + 4x
x = 20, 3x = 60
1 lb. at 20° and 3 lbs. at 100° give a mixture of 80° for
100 - x = 20 + 3x
x = 20, hence the cooler body gains
60°, the warmer one loses 20°.
For both cases Richmann's role holds true:
T = Mt + mt / M + m
(M and T being the mass and temperature of one body, m
and t that of another one.
3. If the substances of two bodies are different, the tem
perature of the cooler one rises more or less according to the
condition of its substance; f. e. 1 lb. of water at 100 and 1 lb.
of mercury at 69° produce a mixture of 99°; 1 lb. of water at
69° and 1 lb. of mercury at 100° give a mixture of 70°. We
see the quantity of heat, which raises the temperature of 1 lb.
of mercury for 30°, raises that of a pound of water only for 1°;
hence water has a 30 times greater capacity to absorb heat
than mercury or a quantity of water having an equal temperature
with the same quantity of mercury contains 30 times more heat
than the latter. Taking the capicity of water for absorbing
heat for 1, we see that the capacity of mercury will be 1/30. That
number, which indicates how many times more heat is contain
ed in one pound of any substance, than in 1 pound of water of
