Page 95 - Physical Chemistry

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500 cm to 1500 cm . (b) What would U and w be if the 2.47 One mole of liquid water at 30°C is adiabatically com-
expansion connects the same initial and final states as in (a) but pressed, P increasing from 1.00 to 10.00 atm. Since liquids and
is done by having the perfect gas expand into vacuum? solids are rather incompressible, it is a fairly good approxima-
tion to take V as unchanged for this process. With this approx-
2.39 One mole of He gas with C V,m 3R/2 essentially inde- imation, calculate q, U, and H for this process.
pendent of temperature expands reversibly from 24.6 L and
300 K to 49.2 L. Calculate the final pressure and temperature if 2.48 The molar heat capacity of oxygen at constant pressure
the expansion is (a) isothermal; (b) adiabatic. (c) Sketch these for temperatures in the range 300 to 400 K and for low or mod-
two processes on a P-V diagram. erate pressures can be approximated as C P,m a bT, where
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a 6.15 cal mol 1 K 1 and b 0.00310 cal mol 1 K .
2.40 For N (g), C is nearly constant at 3.5R 29.1 J/(mol K)
2 P,m (a) Calculate q, w, U, and H when 2.00 mol of O is re-
for temperatures in the range 100 to 400 K and low or moderate 2
versibly heated from 27°C to 127°C with P held fixed at
pressures. (a) Calculate q, w, U, and H for the reversible
1.00 atm. Assume perfect-gas behavior. (b) Calculate q, w, U,
adiabatic compression of 1.12 g of N (g) from 400 torr and
2 and H when 2.00 mol of O initially at 1.00 atm is reversibly
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1000 cm to a final volume of 250 cm . Assume perfect-gas be- 2
heated from 27°C to 127°C with V held fixed.
havior. (b) Suppose we want to cool a sample of N (g) at room
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T and P (25°C and 101 kPa) to 100 K using a reversible adia- 2.49 For this problem use 333.6 J/g and 2256.7 J/g as the la-
batic expansion. What should the final pressure be? tent heats of fusion and vaporization of water at the normal
melting and boiling points, c 4.19 J g 1 K 1 for liquid
P
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2.41 Find q, w, U, and H if 2.00 g of He(g) with C V,m R water, r 0.917 g/cm for ice at 0°C and 1 atm, r 1.000 g/cm 3
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essentially independent of temperature undergoes (a) a re- and 0.958 g/cm for water at 1 atm and 0°C and 100°C, respec-
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versible constant-pressure expansion from 20.0 dm 3 to tively. (For liquid water, c varies slightly with T. The value
P
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40.0 dm at 0.800 bar; (b) a reversible heating with P going given is an average over the range 0°C to 100°C; see Fig. 2.15.)
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from 0.600 bar to 0.900 bar while V remains fixed at 15.0 dm .
Calculate q, w, U, and H for (a) the melting of 1 mol of ice
at 0°C and 1 atm; (b) the reversible constant-pressure heating
Section 2.9 of 1 mol of liquid water from 0°C to 100°C at 1 atm; (c) the
2.42 True or false? (a) A thermodynamic process is defined vaporization of 1 mol of water at 100°C and 1 atm.
by the final state and the initial state. (b) T 0 for every
isothermal process. (c) Every process that has T 0 is an 2.50 Calculate U and H for each of the following changes
isothermal process. (d) U 0 for a reversible phase change at in state of 2.50 mol of a perfect monatomic gas with C V,m
constant T and P. (e) q must be zero for an isothermal process. 1.5R for all temperatures: (a) (1.50 atm, 400 K) → (3.00 atm,
(f) T must be zero for an adiabatic process. 600 K); (b) (2.50 atm, 20.0 L) → (2.00 atm, 30.0 L);
(c) (28.5 L, 400 K) → (42.0 L, 400 K).
2.43 State whether each of the following is a property of a
thermodynamic system or refers to a noninfinitesimal process: 2.51 Can q and w be calculated for the processes of Prob. 2.50?
(a) q; (b) U; (c) H; (d) w; (e) C ; ( f ) m ; (g) H. If the answer is yes, calculate them for each process.
V JT
2.44 Give the value of C [Eq. (2.50)] for (a) the melting of 2.52 For a certain perfect gas, C V,m 2.5R at all tempera-
pr
ice at 0°C and 1 atm; (b) the freezing of water at 0°C and 1 atm; tures. Calculate q, w, U, and H when 2.00 mol of this gas
(c) the reversible isothermal expansion of a perfect gas; (d) the undergoes each of the following processes: (a) a reversible
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reversible adiabatic expansion of a perfect gas. isobaric expansion from (1.00 atm, 20.0 dm ) to (1.00 atm,
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40.0 dm ); (b) a reversible isochoric change of state from
2.45 (This problem is especially instructive.) For each of the 3 3
(1.00 atm, 40.0 dm ) to (0.500 atm, 40.0 dm ); (c) a reversible
following processes deduce whether each of the quantities q, w, 3
isothermal compression from (0.500 atm, 40.0 dm ) to
U, and H is positive, zero, or negative. (a) Reversible melt- 3
(1.00 atm, 20.0 dm ). Sketch each process on the same P-V di-
ing of solid benzene at 1 atm and the normal melting point.
agram and calculate q, w, U, and H for a cycle that consists
(b) Reversible melting of ice at 1 atm and 0°C. (c) Reversible
of steps (a), (b), and (c).
adiabatic expansion of a perfect gas. (d) Reversible isothermal
expansion of a perfect gas. (e) Adiabatic expansion of a perfect Section 2.11
gas into a vacuum (Joule experiment). (f ) Joule–Thomson adi-
2.53 Classify each of the following as kinetic energy, poten-
abatic throttling of a perfect gas. (g) Reversible heating of a
tial energy, or both: (a) translational energy; (b) rotational
perfect gas at constant P. (h) Reversible cooling of a perfect gas
energy; (c) vibrational energy; (d) electronic energy.
at constant V.
2.54 Explain why C of He gas at 10 K and 1 atm is larger
2.46 For each process state whether each of q, w, and U is 5 P,m
than R.
positive, zero, or negative. (a) Combustion of benzene in a 2
sealed container with rigid, adiabatic walls. (b) Combustion of 2.55 (a) Calculate the volume of 1 mole of ideal gas at 25°C
benzene in a sealed container that is immersed in a water bath and 1 atm. Let the gas be in a cubic container. If the gas mol-
at 25°C and has rigid, thermally conducting walls. (c) Adiabatic ecules are distributed uniformly in space with equal spacing
expansion of a nonideal gas into vacuum. between adjacent molecules (of course, this really isn’t so), the