3.5 The Third Law of Thermodynamics and Absolute Entropies 149
b.A sample of water is boiled at 100◦C and 1.00 atm.
c.A sample of supercooled liquid water at− 10 ◦Cis
allowed to equilibrate adiabatically at constant
pressure after a tiny crystal of ice is dropped into it.
d.A sample of an ideal gas expands irreversibly and
adiabatically into a vacuum, as in the Joule experiment.
e.A sample of gas is heated at constant volume.
f.A sample of gas is heated at constant pressure.
g.A sample of gas expands reversibly at constant
temperature.
h.A sample of gas expands reversibly and adiabatically.
3.49Assume that an automobile engine burns 2,2,4-trimethyl
pentane (iso-octane), forming only CO 2 (g) and H 2 O(g).
The density of iso-octane is 0.6909 g mL−^1 , and 1.00
gallon is approximately equal to 3.76 L.
a.Find the amount of heat that can be obtained from
combustion of 1.000 gallon of iso-octane. Ignore the
temperature dependence of∆Hof the combustion
reaction.
b.If the combustion temperature is 2200◦C and the
exhaust temperature is 800◦C, find the maximum
height to which an automobile of 1000.0 kg can be
lifted by combustion of 1.000 gallon of iso-octane.
Ignore all forms of friction. State any assumptions.
c.In some countries, antipollution laws require that the
combustion temperature of automobile engines be
lowered by exhaust gas recirculation, in an attempt to
reduce the amount of nitrogen oxides produced. Repeat
part b with a combustion temperature of 1800◦C.
3.50Construct an accurate graph of each of the following:
a.Sm◦(T)−S◦m(100 K) for a monatomic ideal gas with
CV, m 3 R/2 as a function of temperature from 100 K
to 300 K.
b.Sm(Vm)−Sm(1.000 L) of an ideal gas as a function of
Vmfrom 1.000 L mol−^1 to 10.00 L mol−^1 at a constant
temperature of 300 K.
c.Sm◦(T)−S◦m(223.15 K) for water as a function of
temperature from 223.15 K to 323.15 K.
3.51Label each of the following statements as true or false. If a
statement is true only under certain conditions, label it as
false.
a.The entropy of any system must increase when an
irreversible process occurs.b.The entropy of the surroundings must increase when
an irreversible process occurs.
c.The entropy of the universe must increase when an
irreversible process occurs.
d.The entropy of any system remains constant when a
reversible process occurs.
e.The entropy of the surroundings remains constant
when a reversible process occurs.
f.The entropy of the universe remains constant when a
reversible process occurs.
g.The energy of an isolated system remains constant
when a reversible process occurs in the system.
h.The energy of an isolated system decreases when a
reversible process occurs in the system.
3.52A steam engine has an efficiency that is 55% as large as
that of a Carnot engine. If its boiler is at 250◦C and its
exhaust is at 100◦C, calculate the height to which it can lift
a 1000 kg mass near the earth’s surface if it burns 5.00 kg
of coal. Pretend that the coal is pure graphite and that its
enthalpy change of combustion is equal to that at 25◦C.
3.53Assume that naturally occurring chlorine is 75%^35 Cl and
25%^37 Cl.
a.Calculate the entropy of mixing in 1.00 mol of atomic
chlorine.
b.Assume that you have 1.00 mol of carbon tetrachloride
in which the chlorine isotopes are randomly mixed.
Assume that all of the carbon atoms are^12 C. How
many different kinds of molecules are there, and what
is the amount in moles of each kind of molecule?
c.Find the entropy of mixing of the 1.00 mol of carbon
tetrachloride.
3.54The calculation of the statistical entropy of a metastable
disordered ice crystal is a famous problem that has not yet
been solved exactly. Each water molecule has an oxygen
atom with two hydrogens covalently bonded (at a smaller
distance) and two hydrogens on other molecules hydrogen
bonded to it (at a larger distance). A large number of
coordinate states can be generated by moving the
hydrogens around. For example, if one of the
hydrogen-bonded hydrogens is brought closer to a given
oxygen and covalently bonded to it, one of the covalently
bonded hydrogens must move farther away and become
hydrogen bonded. Make a crude first estimate of the
statistical entropy of a disordered ice crystal containing
1.000 mol of water molecules by pretending that each