Page 94 - Physical Chemistry

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transferred to such parts of the surroundings as the rocks at the enthalpy, change in enthalpy, internal energy, force times
base of the falls.) (b) Calculate the maximum possible internal- length?
6
energy increase of the 2.55 10 L that falls each second. 2.26 The state function H used to be called “the heat content.”
(Before it reaches the falls, more than half the water of the (a) Explain the origin of this name. (b) Why is this name mis-
Niagara River is diverted to a canal or underground tunnels for leading?
use in hydroelectric power plants beyond the falls. These plants
9
generate 4.4 10 W. A power surge at one of these plants led 2.27 We showed H q for a constant-pressure process.
to the great blackout of November 9, 1965, which left 30 mil- Consider a process in which P is not constant throughout the
lion people in the northeast United States and Ontario, Canada, entire process, but for which the final and initial pressures are
without power for many hours.) equal. Need H be equal to q here? (Hint: One way to answer
this is to consider a cyclic process.)
2.18 Imagine an isolated system divided into two parts, 1 and
2, by a rigid, impermeable, thermally conducting wall. Let heat 2.28 A certain system is surrounded by adiabatic walls. The
q flow into part 1. Use the first law to show that the heat flow system consists of two parts, 1 and 2. Each part is closed, is held
1
for part 2 must be q q . at constant P, and is capable of P-V work only. Apply H q
2 1 P
to the entire system and to each part to show that q q 0
2.19 Sometimes one sees the notation q and w for the heat for heat flow between the parts. 1 2
flow into a system and the work done during a process. Explain
why this notation is misleading.
Section 2.6
2.20 Explain how liquid water can go from 25°C and 1 atm to 2.29 True or false? (a) C is a state function. (b) C is an
P P
30°C and 1 atm in a process for which q 0. extensive property.
1
2
2.21 The potential energy stored in a spring is kx , where k 2.30 (a) For CH (g) at 2000 K and 1 bar, C P,m 94.4 J mol 1
2
4
1
is the force constant of the spring and x is the distance the K . Find C of 586 g of CH (g) at 2000 K and 1 bar. (b) For
4
P
spring is stretched from equilibrium. Suppose a spring with C(diamond), C P,m 6.115 J mol 1 K 1 at 25°C and 1 bar. For
force constant 125 N/m is stretched by 10.0 cm, placed in 112 g a 10.0-carat diamond, find c and C . One carat 200 mg.
P
P
of water in an adiabatic container, and released. The mass of the 2.31 For H O(l) at 100°C and 1 atm, r 0.958 g/cm . Find
3
2
spring is 20 g, and its specific heat capacity is 0.30 cal/(g °C). the specific volume of H O(l) at 100°C and 1 atm.
The initial temperature of the water and the spring is 18.000°C. 2
The water’s specific heat capacity is 1.00 cal/(g °C). Find the Section 2.7
final temperature of the water.
2.32 (a) What state function must remain constant in the
2.22 Consider a system enclosed in a vertical cylinder fitted Joule experiment? (b) What state function must remain con-
with a frictionless piston. The piston is a plate of negligible stant in the Joule–Thomson experiment?
mass, on which is glued a mass m whose cross-sectional area is 2.33 For air at temperatures near 25°C and pressures in the
the same as that of the plate. Above the piston is a vacuum. range 0 to 50 bar, the m values are all reasonably close to
JT
(a) Use conservation of energy in the form dE syst dE surr 0 0.2°C/bar. Estimate the final temperature of the gas if 58 g of
to show that for an adiabatic volume change dE syst mg dh air at 25°C and 50 bar undergoes a Joule–Thomson throttling to
dK , where dh is the infinitesimal change in piston height, g is a final pressure of 1 bar.
pist
the gravitational acceleration, and dK pist is the infinitesimal
change in kinetic energy of the mass m. (b) Show that the equa- 2.34 Rossini and Frandsen found that, for air at 28°C and
tion in part (a) gives dw irrev P ext dV dK pist for the irre- pressures in the range 1 to 40 atm, ( U / P) 6.08 J mol 1
T
m
1
versible work done on the system, where P ext is the pressure atm . Calculate ( U / V ) for air at (a) 28°C and 1.00 atm;
m T
m
exerted by the mass m on the piston plate. (b) 28°C and 2.00 atm. [Hint: Use (1.35).]
2.23 Suppose the system of Prob. 2.22 is initially in equilib- 2.35 (a) Derive Eq. (2.65). (b) Show that
3
rium with P 1.000 bar and V 2.00 dm . The external mass m JT 1V>C P 21kC V m J kP 12
m is instantaneously reduced by 50% and held fixed thereafter,
so that P ext remains at 0.500 bar during the expansion. After un- where k is defined by (1.44). [Hint: Start by taking ( / P) of
T
dergoing oscillations, the piston eventually comes to rest. The H U PV.]
3
final system volume is 6.00 dm . Calculate w irrev . 2.36 Is m an intensive property? Is m an extensive property?
J J
Section 2.5 Section 2.8
2.24 True or false? (a) The quantities H, U, PV, H, and 2.37 For a fixed amount of a perfect gas, which of these state-
P V all have the same dimensions. (b) H is defined only for ments must be true? (a) U and H each depend only on T. (b) C P
a constant-pressure process. (c) For a constant-volume process is a constant. (c) P dV nR dT for every infinitesimal process.
in a closed system, H U. (d) C P,m C V,m R. (e) dU C dT for a reversible process.
V
2.25 Which of the following have the dimensions of energy: 2.38 (a) Calculate q, w, U, and H for the reversible
force, work, mass, heat, pressure, pressure times volume, isothermal expansion at 300 K of 2.00 mol of a perfect gas from