3.2 Limits of the First Law
3.1.Decide whether the following processes will be sponta-
neous, and why. The “why” can be general, not specific.
(a)Ice melting at 5°C (b)Ice melting at 5°C (c)KBr (s)
dissolving in water (d)An unplugged refrigerator getting
cold (e)A leaf falling from a tree to the ground (f)The reac-
tion Li (s) ^12 F 2 (g) →LiF (s) (g)The reaction H 2 O () →
H 2 (g) ^12 O 2 (g)
3.2.Try to find one additional example of a spontaneous
process that is in fact endothermic; that is, it occurs with an
absorption of heat.
3.3 Carnot Cycle and Efficiency
3.3.Consider the following quantities for a Carnot-type cycle:
Step 1: q850 J, w334 J. Step 2: q0, w115 J.
Step 3: q623 J, w72 J. Step 4: q0, w150 J.
Calculate the efficiency of the cycle.
3.4.Consider the following quantities for a four-step cycle:
Step 1: q445 J, w220 J. Step 2: q0, w99 J.
Step 3: q660 J, w75 J. Step 4: q0, w109 J.
Under what additional conditions for each step will this be a
Carnot-type cycle? What is the efficiency of this process?
3.5.At what temperature is the low-temperature reservoir of
a process that has an efficiency of 0.440 (44.0%) and a high-
temperature reservoir at 150°C?
3.6.What is the efficiency of an engine whose Thighis 100°C
and whose Tlowis 0°C?
3.7.Superheated steam is steam with a temperature greater
than 100°C. Explain the advantages of using superheated
steam to run a steam engine.
3.8.The Carnot cycle is defined as having a certain specific
first step, the isothermal expansion of a gas. Can a Carnot
cycle start at step 2, the adiabatic expansion? Why or why
not? (Hint:See Figure 3.2.)
3.9.How does a perpetual motion machine violate the first
law of thermodynamics?
3.10.A refrigerator is the reverse of an engine: work is per-
formed to remove heat from a system, making it colder. The
efficiency of a refrigerator (often termed the “coefficient of
performance”) is defined as q 3 /wcycleTlow/(ThighTlow).
Use this definition to determine the efficiency needed to halve
the absolute temperature. What does your answer imply about
attempts to reach absolute zero?
3.11.Efficiency is given by equations 3.5, 3.6, and 3.10.
Although we deal mostly with ideal gases in the development
of thermodynamics, experimentally we are confined to real
gases. Which of the definitions of eare strictly applicable to
processes involving real gases as well as ideal gases?
3.4 & 3.5 Entropy and the Second Law
3.12.What is the entropy change for the melting of 3.87
moles of bismuth at its melting point of 271.3°C? The heat of
fusion of solid Bi is 10.48 kJ/mol. (Bismuth is one of the few
materials, including water, that is less dense in solid form than
in liquid; therefore, solid Bi floats in liquid Bi, like ice floats in
water.)
3.13.Explain why the statement “No process is 100% effi-
cient” is not the best statement of the second law of thermo-
dynamics.
3.14.What is the change in entropy of 1.00 mole of water as
it is heated reversibly from 0°C to 100°C? Assume that the
heat capacity is constant at 4.18 J/gK.
3.15.The heat capacity of solid gold, Au, is given by the ex-
pressionC25.69 7.32 10 ^4 T4.58 10 ^6 T^2 moJlK
Evaluate the change in entropy for 2.50 moles of Au if the
temperature changes reversibly from 22.0°C to 1000°C.
3.16.One mole of He warms up irreversibly at constant vol-
ume from 45°C to 55°C. Is the change in entropy less than,
equal to, or greater than 0.386 J/K? Explain your answer.
3.17.A normal breath has a volume of about 1 L. The pres-
sure exerted by the lungs to draw air in is about 758 torr. If
the surrounding air is at exactly 1 atm (760 torr), calculate
the change in entropy exerted on a breath of air due to its be-
ing inhaled into the lungs. (Hint:you will have to determine
the number of moles of gas involved.)
3.18.A sample of (ideal) gas from a compressed gas cylinder
goes from 230 atm to 1 atm, with a concurrent change of vol-
ume wherein 1 cm^3 expands to 230 cm^3 in volume. Assume
that the temperature remains (or becomes) the same for the
initial and final states. Calculate the change in entropy for
1 mole of the gas undergoing this process. Does your answer
make sense? Why or why not?
3.19.If a 1-mole sample of a real gas from a compressed gas
cylinder goes from 230 atm to 1 atm and from a volume of
1 cm^3 to 195 cm^3 , what is the entropy change for the ex-
pansion if it is assumed to be isothermal? Does this agree with
the second law of thermodynamics?
3.20.Derive equation 3.20. How does the minus sign show
up?
3.21.In Example 3.3, a heat capacity of 20.78 J/molK was
used, which is 5/2 R. Is this value of the heat capacity justi-
fied? Why?
3.22.What is the entropy of mixing to make 1 mole of air
from its constituent elements? Air can be assumed to be 79%
N 2 , 20% O 2 , and 1% Ar. Assume ideal gas behavior.86 Exercises for Chapter 3
EXERCISES FOR CHAPTER 3