Page 96 - Physical Chemistry

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gas volume can be divided into Avogadro’s number of imagi- T 0 and T T . Which student is correct? What error did
2 1
nary equal-sized cubes, each cube containing a molecule at its the other student make?
center. Calculate the edge length of each such cube. (b) What is
the distance between the centers of the uniformly distributed 2.65 A perfect gas undergoes an expansion process at con-
gas molecules at 25°C and 1 atm? (c) Answer (b) for a gas at stant pressure. Does its internal energy increase or decrease?
25°C and 40 atm. Justify your answer.
2.66 Classify each of the following properties as intensive or
2.56 Estimate C and C at 300 K and 1 atm for (a) Ne(g);
V,m P,m
(b) CO(g). extensive and give the SI units of each: (a) density; (b) U;
(c) H ; (d) C ; (e) c ; ( f) C P,m ; (g) P; (h) molar mass; (i) T.
P
P
m
2.57 Use Fig. 2.15 to decide whether U intermol of liquid water
increases or decreases as T increases. 2.67 A student attempting to remember a certain formula
m
n
comes up with C C TVa /k , where m and n are certain
P
V
integers whose values the student has forgotten and where the
remaining symbols have their usual meanings. Use dimensional
General considerations to find m and n.
2.58 (a) Use Rumford’s data given in Sec. 2.4 to estimate the
2.68 Because the heat capacities per unit volume of gases are
relation between the “old” calorie (as defined in Sec. 2.3) and
small, accurate measurement of C or C for gases is not easy.
the joule. Use 1 horsepower 746 W. (b) The same as P V
Accurate measurement of the heat-capacity ratio g of a gas (for
(a) using Joule’s data given in Sec. 2.4.
example, by measurement of the speed of sound in the gas) is
2.59 Students often make significant-figure errors in taking easy. For gaseous CCl at 0.1 bar and 20°C, experiment gives
4
reciprocals, in taking logs and antilogs, and in taking the dif- g 1.13. Find C P,m and C V,m for CCl (g) at 20°C and 1 bar.
4
ference of nearly equal numbers. (a) For a temperature of
1.8°C, calculate T 1 (where T is the absolute temperature) to 2.69 Give the SI units of each of the following properties
P
the proper number of significant figures. (b) Find the common and state whether each is extensive or intensive. (a) ( V/ T) ;
1
2
2
20
T
m
P
T
P
logs of the following numbers: 4.83 and 4.84; 4.83 10 and (b) V ( V/ T) ; (c) ( V / P) ; (d) ( U/ V) ; (e) ( V/ T ) .
20
4.84 10 . From the results, formulate a rule as to the proper 2.70 State whether or not each of the following quantities is
number of significant figures in the log of a number known to infinitesimally small. (a) V; (b) dw ; (c) ( H/ T) ; (d) V dP.
rev
P
n significant figures. (c) Calculate (210.6 K) 1 (211.5 K) 1
to the proper number of significant figures. 2.71 True or false? (a) H is a state function. (b) C is inde-
V
pendent of T for every perfect gas. (c) U q w for every
2.60 (a) A gas obeying the van der Waals equation of state thermodynamic system at rest in the absence of external fields.
(1.39) undergoes a reversible isothermal volume change from (d)A process in which the final temperature equals the initial
V to V . Obtain the expression for the work w. Check that your temperature must be an isothermal process. (e)For a closed sys-
1 2
result reduces to (2.74) for a 0 b. (b) Use the result of tem at rest in the absence of external fields, U q w.
(a) to find w for 0.500 mol of N expanding reversibly from ( f) U remains constant in every isothermal process in a closed
2
0.400 L to 0.800 L at 300 K. See Sec. 8.4 for the a and b val- system. (g) q 0 for every cyclic process. (h) U 0 for every
ues of N . Compare the result with that found if N is assumed cyclic process. (i) T 0 for every adiabatic process in a closed
2 2
to be a perfect gas. system. (j)A thermodynamic process is specified by specifying
the initial state and the final state of the system. (k)Ifa closed
2.61 (a) If the temperature of a system decreases by 8.0°C,
what is T in kelvins? (b) A certain system has C 5.00 J/°C. system at rest in the absence of external fields undergoes an adi-
P
What is its C in joules per kelvin? abatic process that has w 0, then the system’s temperature
P
must remain constant. (l) P-V work is usually negligible for
2.62 Explain why Boyle’s law PV constant for an ideal gas solids and liquids. (m)If neither heat nor matter can enter or
g
does not contradict the equation PV constant for a revers- leave a system, that system must be isolated. (n)For a closed
ible adiabatic process in a perfect gas with C constant. system with P-V work only, a constant-pressure process that has
V
2
q 0 must have T 0. (o) (1/V) dV ln(V V ). (p) The
2.63 Point out the error in the Sec. 2.12 reasoning that gave 1 2 1
q 0 for a reversible isothermal process in a perfect gas. value of U is independent of the path (process) used to go from
state 1 to state 2. (q)For any process, T t, where T and t are
2.64 A perfect gas with C 3R independent of T expands the Kelvin and Celsius temperatures. (r)If q 0 for a process,
V,m
adiabatically into a vacuum, thereby doubling its volume. Two then the process must be isothermal. (s)For a reversible process,
students present the following conflicting analyses. Genevieve P must be constant. (t) (1/T) dT (ln T )/(ln T ). (u)If the final
T 2
T 1 2 1
1/3
uses Eq. (2.76) to write T /T (V /2V ) R/3R and T T /2 . temperature equals the initial temperature, the process must be an
2 1 1 1 2 1
1
2
Wendy writes U q w 0 0 0 and U C T, so isothermal process. (v) TdT (T T ) .
T 2
V T 1 2 2 1