2
The First Law: the concepts
Solutions to exercises
Discussion questions
E2.1(b)
Work is a transfer of energy that results in orderly motion of the atoms and molecules in a system;
heat is a transfer of energy that results in disorderly motion. See Molecular Interpretation 2.1 for a
more detailed discussion.
E2.2(b)
Rewrite the two expressions as follows:
(1) adiabatic
p
∝
1
/V
γ
(2) isothermal
p
∝
1
/V
The physical reason for the difference is that, in the isothermal expansion, energy flows into the
system as heat and maintains the temperature despite the fact that energy is lost as work, whereas in
the adiabatic case, where no heat flows into the system, the temperature must fall as the system does
work. Therefore, the pressure must fall faster in the adiabatic process than in the isothermal case.
Mathematically this corresponds to
γ >
1.
E2.3(b)
Standard reaction enthalpies can be calculated from a knowledge of the standard enthalpies of forma
tion of all the substances (reactants and products) participating in the reaction. This is an exact method
which involves no approximations. The only disadvantage is that standard enthalpies of formation
are not known for all substances.
Approximate values can be obtained from mean bond enthalpies. See almost any general chemistry
text, for example,
Chemical Principles
, by Atkins and Jones, Section 6.21, for an illustration of the
method of calculation. This method is often quite inaccurate, though, because the average values of
the bond enthalpies used may not be close to the actual values in the compounds of interest.
Another somewhat more reliable approximate method is based on thermochemical groups which
mimic more closely the bonding situations in the compounds of interest. See Example 2.6 for an
illustration of this kind of calculation. Though better, this method suffers from the same kind of
defects as the average bond enthalpy approach, since the group values used are also averages.
Computer aided molecular modeling is now the method of choice for estimating standard reaction
enthalpies, especially for large molecules with complex threedimensional structures, but accurate
numerical values are still difficult to obtain.
Numerical exercises
E2.4(b)
Work done against a uniform gravitational field is
w
=
mgh
(a)
w
=
(
5
.
0 kg
)
×
(
100 m
)
×
(
9
.
81 m s
−
2
)
=
4
.
9
×
10
3
J
(b)
w
=
(
5
.
0 kg
)
×
(
100 m
)
×
(
3
.
73 m s
−
2
)
=
1
.
9
×
10
3
J
E2.5(b)
Work done against a uniform gravitational field is
w
=
mgh
=
(
120
×
10
−
3
kg
)
×
(
50 m
)
×
(
9
.
81 m s
−
2
)
=
59 J
E2.6(b)
Work done
by
a system expanding against a constant external pressure is
w
= −
p
ex
V
= −
(
121
×
10
3
Pa
)
×
(
15 cm
)
×
(
50 cm
2
)
(
100 cm m
−
1
)
3
=
−
91 J
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INSTRUCTOR
’
S MANUAL
E2.7(b)
For a perfect gas at constant temperature
U
=
0
so
q
= −
w
For a perfect gas at constant temperature,
H
is also
zero
d
H
=
d
(U
+
pV )
we have already noted that
U
does not change at constant temperature; nor does
pV
if the gas obeys
Boyle’s law. These apply to all three cases below.
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 Trigraph, Adiabatic process, kJ mol1

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