Page 126 - Physical Chemistry

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3.29 Estimate the volume of cooling water used per minute 3.36 In the tropics, water at the surface of the ocean is warmer
by a 1000-MW power plant whose efficiency is 40%. Assume than water well below the surface. Someone proposes to draw
that the cooling water undergoes a 10°C temperature rise (a heat from the warm surface water, convert part of it to work,
typical value) when it cools the steam. and discard the remainder to cooler water below the surface.
Does this proposal violate the second law?
3.30 A certain perfect gas has C V,m a bT, where a 25.0
2
J/(mol K) and b 0.0300 J/(mol K ). Let 4.00 mol of this gas 3.37 Use (3.15) to show that it is impossible to attain the ab-
go from 300 K and 2.00 atm to 500 K and 3.00 atm. Calculate solute zero of temperature.
each of the following quantities for this change of state. If it is
impossible to calculate a quantity from the given information, 3.38 Suppose that an infinitesimal crystal of ice is added to
state this. (a) q; (b) w; (c) U; (d) H; (e) S. 10.0 g of supercooled liquid water at 10.0°C in an adiabatic
container and the system reaches equilibrium at a fixed pressure
3.31 Classify each of these processes as reversible or irre- of 1 atm. (a) What is H for the process? (b) The equilibrium
versible: (a) freezing of water at 0°C and 1 atm; (b) freezing of state will contain some ice and will therefore consist either of
supercooled water at 10°C and 1 atm; (c) burning of carbon ice plus liquid at 0°C or of ice at or below 0°C. Use the answer
in O to give CO at 800 K and 1 atm; (d) rolling a ball on a to (a) to deduce exactly what is present at equilibrium. (c) Calcu-
2
2
floor with friction; (e) the Joule–Thomson experiment; ( f) adi- late S for the process. (See Prob. 2.49 for data.)
abatic expansion of a gas into vacuum (the Joule experiment); 3.39 Give the SI units of (a) S; (b) S ; (c) q; (d) P; (e) M
(g) use of a frictionless piston to infinitely slowly increase the (molecular weight); (f) M (molar mass). m r
pressure on an equilibrium mixture of N , H , and NH , thereby
2
3
2
shifting the equilibrium. 3.40 Which of the following statements can be proved from
the second law of thermodynamics? (a) For any closed system,
3.32 For each of the following pairs of systems, state which equilibrium corresponds to the position of maximum entropy of
system (if either) has the greater U and which has the greater S. the system. (b) The entropy of an isolated system must remain
(a) 5 g of Fe at 20°C and 1 atm or 10 g of Fe at 20°C and 1 atm; constant. (c) For a system enclosed in impermeable adiabatic
(b) 2 g of liquid water at 25°C and 1 atm or 2 g of water vapor walls, the system’s entropy is maximized at equilibrium. (d) The
at 25°C and 20 torr; (c) 2 g of benzene at 25°C and 1 bar or 2 g entropy of a closed system can never decrease. (e) The entropy
of benzene at 40°C and 1 bar; (d) a system consisting of 2 g of of an isolated system can never decrease.
metal M at 300 K and 1 bar and 2 g of M at 310 K and 1 bar or
a system consisting of 4 g of M at 305 K and 1 bar. Assume the 3.41 True or false? (a) For every process in an isolated sys-
specific heat of M is constant over the 300 to 310 K range and tem, T 0. (b) For every process in an isolated system that
the volume change of M is negligible over this range; (e) 1 mol has no macroscopic kinetic or potential energy, U 0. (c) For
of a perfect gas at 0°C and 1 atm or 1 mol of the same perfect every process in an isolated system, S 0. (d) If a closed sys-
gas at 0°C and 5 atm. tem undergoes a reversible process for which V 0, then the
P-V work done on the system in this process must be zero.
3.33 Which of these cyclic integrals must vanish for a closed
(e) S when 1 mol of N (g) goes irreversibly from 25°C and
system with P-V work only? (a) P dV; (b) (P dV V dP); 2
10 L to 25°C and 20 L must be the same as S when 1 mol of
(c) V dV; (d) dq /T; (e) H dT; (f ) dU; (g) dq ;
rev rev N (g) goes reversibly from 25°C and 10 L to 25°C and 20 L.
(h) dq ; (i) dw ; (j) dw /P. 2
P rev rev ( f) S 0 for every adiabatic process in a closed system.
3.34 Consider the following quantities: C , C , R (the gas (g)For every reversible process in a closed system, S H/T.
P P,m
constant), k (Boltzmann’s constant), q, U/T. (a) Which have (h) A closed-system process that has T 0, must have U
the same dimensions as S? (b) Which have the same dimen- 0. (i) For every isothermal process in a closed system, S
sions as S ? H/T. (j) q 0 for every isothermal process in a closed system.
m
(k) In every cyclic process, the final and initial states of the sys-
3.35 What is the relevance to thermodynamics of the following tem are the same and the final and initial states of the sur-
refrain from the Gilbert and Sullivan operetta H.M.S. Pinafore? roundings are the same.
“What, never? No, never! What, never? Well, hardly ever!”

REVIEW PROBLEMS

R3.1 For a closed system, give an example of each of the fol- R3.2 State what experimental data you would need to look up
lowing. If it is impossible to have an example of the process, to calculate each of the following quantities. Include only the
state this. (a) An isothermal process with q
0. (b) An adia- minimum amount of data needed. Do not do the calculations.
batic process with T
0. (c) An isothermal process with (a) U and H for the freezing of 653 g of liquid water at 0°C
U
0. (d) A cyclic process with S
0. (e) An adiabatic and 1 atm. (b) S for the melting of 75 g of Na at 1 atm and its
process with S
0. (f ) A cyclic process with w
0. normal melting point. (c) U and H when 2.00 mol of O gas
2