Page 66 - Physical chemistry eng

NUMERICAL PROBLEMS 43

process in a P–V diagram. Calculate w for each step and for the P2.28 A 3.50 mole sample of an ideal gas with C V,m = 3R>2
total process. What values for w would you calculate if the cycle is expanded adiabatically against a constant external pres-
were traversed in the opposite direction? sure of 1.45 bar. The initial temperature and pressure are
P2.20 In an adiabatic compression of one mole of an ideal T = 310. K and P = 15.2 bar . The final pressure is
i
i
gas with C V,m = 5R>2 , the temperature rises from 278 K to P = 1.45 bar . Calculate q, w, ¢U , and ¢H for the process.
f
450. K. Calculate q, w, ¢H , and ¢U . P2.29 A nearly flat bicycle tire becomes noticeably warmer
P2.21 The heat capacity of solid lead oxide is given by after it has been pumped up. Approximate this process as a
reversible adiabatic compression. Assume the initial pressure
T -1 -1
-3
C P,m = 44.35 + 1.47 * 10 in units of J K mol and temperature of the air before it is put in the tire to be
K
P = 1.00 bar and T = 280. K The final pressure in the tire
i
i
Calculate the change in enthalpy of 1.75 mol of PbO(s) if it is is P = 3.75 bar . Calculate the final temperature of the air in
f
cooled from 825 K to 375 K at constant pressure. the tire. Assume that C V,m = 5R>2 .
P2.22 A 2.25 mole sample of carbon dioxide, for which P2.30 For 1.25 mol of an ideal gas, P external = P =
-1
C P,m = 37.1 J K mol -1 at 298 K, is expanded reversibly 350. * 10 Pa . The temperature is changed from 135°C to
3
and adiabatically from a volume of 4.50 L and a temperature 21.2°C, and C V,m = 3R>2 . Calculate q, w, ¢U , and ¢H .
of 298 K to a final volume of 32.5 L. Calculate the final tem-
P2.31 Suppose an adult is encased in a thermally insulating
perature, q, w, ¢H , and ¢U . Assume that C P,m is constant barrier so that all the heat evolved by metabolism of food-
over the temperature interval.
stuffs is retained by the body. What is her temperature
P2.23 A 1.75 mole sample of an ideal gas for which increase after 2.5 hours? Assume the heat capacity of the
P = 2.50 bar and T = 335 K is expanded adiabatically body is 4.18 J g K and that the heat produced by metabo-
–1 –1
–1
–1
against an external pressure of 0.225 bar until the final pres- lism is 9.4 kJ kg hr .
sure is 0.225 bar. Calculate the final temperature, q, w, ¢H ,
P2.32 Consider the isothermal expansion of 2.35 mol of an
and ¢U for (a) C V,m = 3R>2 , and (b) C V,m = 5R>2 . ideal gas at 415 K from an initial pressure of 18.0 bar to a
P2.24 A 3.50 mole sample of N 2 in a state defined by T = final pressure of 1.75 bar. Describe the process that will
i
250. K and V = 3.25 L undergoes an isothermal reversible result in the greatest amount of work being done by the sys-
i
expansion until V = 35.5 L Calculate w, assuming (a) that tem with P external Ú 1.75 bar , and calculate w. Describe the
f
the gas is described by the ideal gas law, and (b) that the gas process that will result in the least amount of work being
is described by the van der Waals equation of state. What is done by the system with P external Ú 1.75 bar , and calculate
the percent error in using the ideal gas law instead of the van w. What is the least amount of work done without restric-
der Waals equation? The van der Waals parameters for N 2 are tions on the external pressure?
listed in Table 7.4. 3
P2.33 An automobile tire contains air at 225 * 10 Pa at
P2.25 A major league pitcher throws a baseball with a 25.0°C. The stem valve is removed and the air is allowed to
speed of 162 kilometers per hour. If the baseball weighs expand adiabatically against the constant external pressure of
–1
235 grams and its heat capacity is 1.7 J g –1 K , calculate the one bar until P = P external . For air, C V,m = 5R>2 . Calculate
temperature rise of the ball when it is stopped by the catcher’s the final temperature. Assume ideal gas behavior.
mitt. Assume no heat is transferred to the catcher’s mitt and
P2.34 One mole of an ideal gas is subjected to the following
that the catcher’s arm does not recoil when he or she catches
changes. Calculate the change in temperature for each case if
the ball. Also assume that the kinetic energy of the ball is
C V,m = 3R>2 .
completely converted into thermal energy.
a. q =-425 J, w = 185 J
P2.26 A 2.50 mol sample of an ideal gas for which
b. q = 315. J, w =-315 J
C V,m = 3R>2 undergoes the following two-step process:
(1) From an initial state of the gas described by T = 13.1°C c. q = 0, w = 225 J
5
and P = 1.75 * 10 Pa , the gas undergoes an isothermal P2.35 Consider the adiabatic expansion of 0.500 mol of an
4
expansion against a constant external pressure of 3.75 * 10 Pa ideal monatomic gas with C V,m = 3R>2 . The initial state is
until the volume has doubled. (2) Subsequently, the gas is cooled described by P = 6.25 bar and T = 300. K .
at constant volume. The temperature falls to – 23.6°C. Calculate a. Calculate the final temperature if the gas undergoes a
q, w, ¢U , and ¢H for each step and for the overall process. reversible adiabatic expansion to a final pressure of
P2.27 A 2.35 mole sample of an ideal gas, for which C V,m = P = 1.25 bar .
6
3R>2 , initially at 27.0°C and 1.75 * 10 Pa , undergoes a two- b. Calculate the final temperature if the same gas undergoes
stage transformation. For each of the stages described in the fol- an adiabatic expansion against an external pressure of
lowing list, calculate the final pressure, as well as q, w, ¢U , and P = 1.25 bar to a final pressure P = 1.25 bar .
¢H . Also calculate q, w, ¢U , and ¢H for the complete process. Explain the difference in your results for parts (a) and (b).
a. The gas is expanded isothermally and reversibly until the P2.36 A pellet of Zn of mass 31.2 g is dropped into a flask
volume triples. containing dilute H SO 4 at a pressure of P = 1.00 bar and a
2
b. Beginning at the end of the first stage, the temperature is temperature of T = 300. K . What is the reaction that occurs?
raised to 105°C at constant volume. Calculate w for the process.