2.3 Internal Energy: The First Law of Thermodynamics 55
pressure of 1.000 atm. Neglect the volume of the liquid
compared with that of the vapor.2.16A sample of 2.000 mol of CO 2 gas is heated from 0.00◦Cto
100.0◦C at a constant pressure of 1.000 atm. Findqandw
for this process. State any assumptions or approximations.
a.Assume thatCP, mis constant and equal to its value in
Table A.8 at 298.15 K. Assume that the gas is ideal.
b.Assume thatCP, mis given by the formula in Table A.6
with the parameters given there and that the gas is
described by the truncated pressure virial equation of
state:PVmRT+A 2 Pand use the fact thatA 2 B 2.2.3 Internal Energy: The First Law of
Thermodynamics
Although Lavoisier discredited the phlogiston theory of combustion, which held that
combustion was the loss of an “imponderable” fluid calledphlogiston, he was one of
the principal promoters of the equally incorrectcaloric theory of heatespoused by
Black, which asserted that heat was an imponderable fluid called “caloric.” The first
experimental studies that discredited the caloric theory were done by Count Rumford.
Rumford was at one time in charge of manufacturing cannons for the Elector of Bavaria,
the ruler who made him a count. Rumford noticed that when a cannon was bored with
a dull boring tool, more heat was produced than when a sharp tool was used. He carried
out a systematic set of experiments and was able to show by using a very dull tool that
there was no apparent limit to the amount of heat that could be generated by friction. He
immersed the cannon in water to transfer the heat from the cannon and even generated
enough heat to have melted the cannon. Rumford’s results showed that “caloric” was
not simply being extracted from the cannon, because if caloric existed only a definite
amount could be stored in a cannon without melting it. Work must have been converted
to heat.
Benjamin Thompson, Count Rumford,
1753–1814, was an American-
British physicist who abandoned his
family and left America after the
American revolution because of his
royalist sympathies. He pursued a
checkered career in various countries,
including Bavaria (where he ingratiated
himself with the Elector of Bavaria),
France (where he married Lavoisier’s
widow), and England (where he
founded the Royal Institution and hired
Humphrey Davy as a lecturer).
Rumford calculated an approximate value for the “mechanical equivalent of heat,”
or the amount of heat to which a joule of work could be converted. Better values
were obtained by Mayer in 1842 and Joule in 1847. Joule carried out experiments in
which changes of temperature were produced either by doing work on a system or
by heating it. His apparatus is schematically depicted in Figure 2.4. A falling mass
turned a stirring paddle in a sample of water, doing work on the liquid. The rise in
temperature of the water was measured and the amount of work done by the falling
mass was compared with the amount of heat required to produce the same change in
temperature. Joule found that the ratio of the work to the amount of heat was always
the same, approximately 4.18 J of work for 1.00 cal of heat. The calorie is now defined
to be exactly 4.184 J.Julius Robert Mayer, 1814−1878, was a
German physicist originally trained as a
physician. He was apparently the first to
assert that heat and work are two
different means by which energy is
transferred, and that energy can neither
be created nor destroyed.
EXAMPLE2.12
Calculate the rise in temperature of 100.0 g of water if the falling weight of Figure 2.4 has a
mass of 5.00 kg and drops by 0.800 m. Neglect friction in the pulleys.
Solution
LetVbe the potential energy of the mass.∆V(5.00 kg)(9.80 ms−^2 )(− 0 .800 m)− 39 .2J