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process state whether each of U, S, S univ , and A is posi- Wagner, J. Phys. Chem. Ref. Data, 18, 1537 (1989); P. G. Hill,
tive, zero, or negative. ibid., 19, 1233 (1990).]
4.47 For each of the following processes, state which of U, 4.55 When 3.00 mol of a certain gas is heated reversibly from
H, S, S univ , A, and G must be zero. (a) A nonideal gas 275 K and 1 bar to 375 K and 1 bar, S is 20.0 J/K. If 3.00 mol
undergoes a Carnot cycle. (b) Hydrogen is burned in an adia- of this gas is heated irreversibly from 275 K and 1 bar to 375 K
batic calorimeter of fixed volume. (c) A nonideal gas undergoes and 1 bar, will S be less than, the same as, or greater than
a Joule–Thomson expansion. (d) Ice is melted at 0°C and 1 atm. 20.0 J/K?
4.56 For each of the following sets of quantities, all the quan-
4.48 Give an example of a liquid with a negative (
U/
V) .
T
tities except one have something in common. State what they
4.49 Give the name of each of these Greek letters and state the have in common and state which quantity does not belong with
thermodynamic quantity that each stands for: (a) n; (b) m; (c) j; the others. (In some cases, more than one answer for the prop-
(d) a; (e) k; ( f ) r. erty in common might be possible.) (a) C , C , U, T, S, G, A, V;
P
V
(b) H, U, G, S, A.
4.50 Give the conditions of applicability of each of these
equations: (a) dU dq dw; (b) dU TdS PdV; (c) dU 4.57 For each of the following statements, tell which state
a
a
TdS PdV m dn . function(s) is (are) being described. (a) It enables one to find the
i
i
i
a
rates of change of enthalpy and of entropy with respect to tem-
4.51 Give the SI units of (a) G; (b) S ; (c) C ; (d) m . perature at constant pressure. (b) They determine whether sub-
i
m
P
stance i in phase a is in phase equilibrium with i in phase b.
4.52 For a closed system with P-V work only, (a) write the
equation that gives the condition of phase equilibrium; (b) write (c) It enables one to find the rates of change of U and of S with
the equation that gives the condition of reaction equilibrium. respect to T at constant V. (d) It is maximized when an isolated
(c) Explain why dG 0 is not the answer to (a) and (b). system reaches equilibrium. (e) It is maximized when a system
reaches equilibrium. (f) It is minimized when a closed system
4.53 For a closed system with P-V work only and held at con- capable of P-V work only and held at constant T and P reaches
stant T and P, show that dS dq/T dG/T for an irreversible equilibrium.
material change. (Hint: Start with G H TS.)
4.58 True or false? (a) C P,m C V,m R for all gases. (b) C P
2
4.54 An equation for G of a pure substance as a function C TVa /k for every substance. (c) G is always zero for
m
V
of T and P (or of A as a function of T and V) is called a a reversible process in a closed system capable of P-V work
m
fundamental equation of state. From a fundamental equation only. (d) The Gibbs energy of a closed system with P-V work
of state, one can calculate all thermodynamic properties of a only is always minimized at equilibrium. (e) The work done by
substance. Express each of the following properties in terms of a closed system can exceed the decrease in the system’s internal
2
2
2
2
G , T, P, (
G /
T ) , (
G /
P) , (
G /
T ) , (
G /
P ) , energy. ( f) For an irreversible, isothermal, isobaric process in a
T
m
P
m
T
P
m
m
m
2
and
G /
P
T. (a) S ; (b) V ; (c) H ; (d) U ; (e) C P,m ; ( f) closed system with P-V work only, G must be negative. (g) G syst
m
m
m
m
m
C V ,m ; (g) a; (h) k. [Using Eqs. like (4.60) and (4.63) for H and G surr is constant for any process. (h) S is positive for every
S and experimental C , a, and k data, one can construct a fun- irreversible process. (i) S syst S surr is positive for every ir-
P
damental equation of state of the form G f(T, P), where U reversible process. (j) (TS) S T T S. (k) (U TS)
m
and S have each been arbitrarily assigned a value of zero in U (TS). (l) (
V/
T ) V/ T for a constant-pressure
P
some reference state, which is usually taken as the liquid at the process. (m) If a system remains in thermal and mechanical
triple point. Accurate fundamental equations of state have been equilibrium during a process, then its T and P are constant dur-
constructed for several fluids. For fluid H O, fundamental equa- ing the process. (n) The entropy S of a closed system with P-V
2
tions of state contain about 50 parameters whose values are ad- work only is always maximized at equilibrium. (o) If a b,
justed to give good fits of experimental data; see A. Saul and W. then we must have ka kb, where k is a nonzero constant.