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FURTHER READING Problems

Denbigh, pp. 21–42, 48–60; Kestin, chap. 9; Zemansky and Dittman, chaps. 6, 7, 8.

PROBLEMS

Section 3.2 1 bar is equal to the molar entropy of 10 g of H O(l) at 300 K
2
3.1 True or false? (a) Increasing the temperature of the hot and 1 bar. ( f) For a reversible isothermal process in a closed
1
2
reservoir of a Carnot-cycle engine must increase the efficiency system, S must be zero. (g) The integral T C dT in
V
1
of the engine. (b) Decreasing the temperature of the cold reser- Eq. (3.30) is always equal to C ln (T /T ). (h) The system’s en-
2
V
1
voir of a Carnot-cycle engine must increase the efficiency of the tropy change for an adiabatic process in a closed system must
engine. (c) A Carnot cycle is by definition a reversible cycle. be zero. (i) Thermodynamics cannot calculate S for an irre-
(d) Since a Carnot cycle is a cyclic process, the work done in a versible process. (j) For a reversible process in a closed system,
Carnot cycle is zero. dq is equal to T dS. (k) The formulas of Sec. 3.4 enable us to
calculate S for various processes but do not enable us to find
3.2 Consider a heat engine that uses reservoirs at 800°C and the value of S of a thermodynamic state.
0°C. (a) Calculate the maximum possible efficiency. (b) If q is
H
1000 J, find the maximum value of w and the minimum value 3.8 The molar heat of vaporization of Ar at its normal boiling
of q . point 87.3 K is 1.56 kcal/mol. (a) Calculate S for the vapor-
C
ization of 1.00 mol of Ar at 87.3 K and 1 atm. (b) Calculate S
3.3 Suppose the coldest reservoir we have at hand is at 10°C. when 5.00 g of Ar gas condenses to liquid at 87.3 K and 1 atm.
If we want a heat engine that is at least 90% efficient, what is
the minimum temperature of the required hot reservoir? 3.9 Find S when 2.00 mol of O is heated from 27°C to
2
127°C with P held fixed at 1.00 atm. Use C P,m from Prob. 2.48.
3.4 A Carnot-cycle heat engine does 2.50 kJ of work per
cycle and has an efficiency of 45.0%. Find w, q , and q for one 3.10 Find S for the conversion of 1.00 mol of ice at 0°C and
H
C
cycle. 1.00 atm to 1.00 mol of water vapor at 100°C and 0.50 atm. Use
data from Prob. 2.49.
3.5 Heat pumps and refrigerators are heat engines running in
3.11 Find S when 1.00 mol of water vapor initially at 200°C
reverse; a work input w causes the system to absorb heat q
C
from a cold reservoir at T and emit heat q into a hot reser- and 1.00 bar undergoes a reversible cyclic process for which
C H
voir at T . The coefficient of performance K of a refrigerator is q 145 J.
H
q /w, and the coefficient of performance e of a heat pump is
C 3.12 Calculate S for each of the following changes in state
q /w. (a) For reversible Carnot-cycle refrigerators and heat
H of 2.50 mol of a perfect monatomic gas with C 1.5R for
pumps, express K and e in terms of T and T . (b) Show that V,m
C H all temperatures: (a) (1.50 atm, 400 K) → (3.00 atm, 600 K);
e is always greater than 1. (c) Suppose a reversible heat pump
rev (b) (2.50 atm, 20.0 L) → (2.00 atm, 30.0 L); (c) (28.5 L, 400 K)
transfers heat from the outdoors at 0°C to a room at 20°C. For
→ (42.0 L, 400 K).
each joule of work input to the heat pump, how much heat will
be deposited in the room? (d) What happens to K as T goes 3.13 For N (g), C is nearly constant at 29.1 J/(mol K) for
rev C 2 P,m
to 0 K? temperatures in the range 100 K to 400 K and low or moderate
pressures. Find S for the reversible adiabatic compression of
3.6 Use sketches of the work w done by the system for each 1.12 g of N (g) from 400 torr and 1000 cm to a final volume
3
by
2
step of a Carnot cycle to show that w for the cycle equals the of 250 cm . Assume perfect-gas behavior.
3
by
area enclosed by the curve of the cycle on a P-V plot.
3.14 Find S for the conversion of 10.0 g of supercooled
Section 3.4 water at 10°C and 1.00 atm to ice at 10°C and 1.00 atm.
3.7 True or false? (a) A change of state from state 1 to state 2 Average c values for ice and supercooled water in the range
P
produces a greater increase in entropy when carried out irre- 0°C to 10°C are 0.50 and 1.01 cal/(g °C), respectively. See
versibly than when done reversibly. (b) The heat q for an ir- also Prob. 2.49.
reversible change of state from state 1 to 2 might differ from the 3.15 State whether each of q, w, U, and S is negative, zero,
heat for the same change of state carried out reversibly. (c) The or positive for each step of a Carnot cycle of a perfect gas.
higher the absolute temperature of a system, the smaller the in-
crease in its entropy produced by a given positive amount dq rev 3.16 After 200 g of gold [c 0.0313 cal/(g °C)] at 120.0°C
P
of reversible heat flow. (d) The entropy of 20 g of H O(l) at is dropped into 25.0 g of water at 10.0°C, the system is allowed
2
300 K and 1 bar is twice the entropy of 10 g of H O(l) at 300 K to reach equilibrium in an adiabatic container. Find (a) the final
2
and 1 bar. (e) The molar entropy of 20 g of H O(l) at 300 K and temperature; (b) S ; (c) ¢S H 2 O ; (d) ¢S ¢S H 2 O .
Au
Au
2