Page 93 - Physical Chemistry

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PROBLEMS

Section 2.1 2.11 It was stated in Sec. 2.2 that for a given change of state,
2.1 True or false? (a) The kinetic energy of a system of several w rev can have any positive or negative value. Consider a change
particles equals the sum of the kinetic energies of the individ- of state for which P P and V V . For this change of state,
1
2
1
2
ual particles. (b) The potential energy of a system of interacting use a P-V diagram to (a) sketch a process with w rev 0;
particles equals the sum of the potential energies of the indi- (b) sketch a process with w rev 0. Remember that neither P
vidual particles. nor V can be negative.
2.2 Give the SI units of (a) energy; (b) work; (c) volume;
(d) force; (e) speed; ( f ) mass. Section 2.3
2.12 Specific heats can be measured in a drop calorimeter;
2.3 Express each of these units as a combination of meters, here, a heated sample is dropped into the calorimeter and the
kilograms, and seconds: (a) joule; (b) pascal; (c) liter; (d) new- final temperature is measured. When 45.0 g of a certain metal
ton; (e) watt.
at 70.0°C is added to 24.0 g of water (with c 1.00 cal/g-°C)
P
2.4 An apple of mass 155 g falls from a tree and is caught by a at 10.0°C in an insulated container, the final temperature is
small boy. If the apple fell a distance of 10.0 m, find (a) the work 20.0°C. (a) Find the specific heat capacity of the metal. (b) How
done on the apple by the earth’s gravitational field; (b) the kinetic much heat flowed from the metal to the water? Note: In (a), we
energy of the apple just before it was caught; (c) the apple’s are finding the average c over the temperature range of the
P
speed just before it was caught. experiment. To determine c as a function of T, one repeats the
P
experiment many times, using different initial temperatures for
2.5 An apple of mass 102 g is ground up into applesauce the metal.
(with no added sugar) and spread evenly over an area of 1.00 m 2
on the earth’s surface. What is the pressure exerted by the Section 2.4
applesauce?
2.13 True or false? (a) For every process, E syst E surr .
2.6 In the obsolete cgs system of mechanical units, length is (b) For every cyclic process, the final state of the system is the
expressed in centimeters, mass in grams, and time in seconds. same as the initial state. (c) For every cyclic process, the final
The cgs unit of force is the dyne and the cgs unit of energy is state of the surroundings is the same as the initial state of the sur-
the erg. Find the relation between dynes and newtons. Find the roundings. (d) For a closed system at rest with no fields present,
relation between ergs and joules. the sum q w has the same value for every process that goes
from a given state 1 to a given state 2. (e) If systems A and B
each consist of pure liquid water at 1 bar pressure and if
Section 2.2
T T , then the internal energy of system A must be greater
2.7 True or false? (a) The P-V work in a mechanically revers- A B
than that of B.
ible process in a closed system always equals P V. (b) The
symbol w in this book means work done on the system by the 2.14 For which of these systems is the system’s energy con-
surroundings. (c) The infinitesimal P-V work in a mechanically served in every process: (a) a closed system; (b) an open sys-
reversible process in a closed system always equals PdV. tem; (c) an isolated system; (d) a system enclosed in adiabatic
(d) The value of the work w in a reversible process in a closed walls?
system can be found if we know the initial state and the final 3
2
state of the system. (e) The value of the integral PdV is fixed 2.15 One food calorie 10 cal 1 kcal. A typical adult in-
1 gests 2200 kcal/day. (a) Show that an adult uses energy at about
once the initial and final states 1 and 2 and the equation of state
2
P P(T, V) are known. ( f ) The equation w PdV the same rate as a 100-W lightbulb. (b) Calculate the total an-
9
rev 1 nual metabolic-energy expenditure of the 7 10 people on
2
applies only to constant-pressure processes. (g) PdV
20
1 earth and compare it with the 5 10 J per year energy used
2
nR dT for every reversible process in an ideal gas.
1 by the world economy. (Neglect the fact that children use less
2.8 If P 175 torr, V 2.00 L, P 122 torr, V 5.00 L, metabolic energy than adults.)
2
1
2
1
find w rev for process (b) of Fig. 2.3 by (a) finding the area under 2.16 A mole of water vapor initially at 200°C and 1 bar un-
2
the curve; (b) using w rev PdV. dergoes a cyclic process for which w 338 J. Find q for this
1
2.9 A nonideal gas is heated slowly and expands reversibly process.
3
at a constant pressure of 275 torr from a volume of 385 cm to
3
875 cm . Find w in joules. 2.17 William Thomson tells of running into Joule in 1847 at
Mont Blanc; Joule had with him his bride and a long ther-
2.10 Using the P , V , P , and V values of Example 2.2, find mometer with which he was going to “try for elevation of tem-
2
2
1
1
w for a reversible process that goes from state 1 to state 2 in perature in waterfalls.” The Horseshoe Falls at Niagara Falls is
Fig. 2.3 via a straight line (a) by calculating the area under 167 ft high and has a summer daytime flow rate of 2.55
6
2
the curve; (b) by using w rev PdV. [Hint: The equation of 10 L/s. (a) Calculate the maximum possible temperature dif-
1
the straight line that goes through points x , y and x , y is ference between the water at the top and at the bottom of the
2
2
1
1
(y y )/(x x ) (y y )/(x x ).] falls. (The maximum possible increase occurs if no energy is
1
1
2
1
2
1