{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Chapter 5 Problems - Problems “The Conversion of...

Info icon This preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Problems “The Conversion of Energy,” C. M. Summers, Sci. Am September 1971. “Energy Conversion: Better Living Through Themodynamics,” W. D. Metz, Science 188, 820 (1975). “Heat-Fall and Entropy,” J. P. Lowe, J. Chem. Educ, 59, 353 (1982). “Demons, Engines, and the Second Law,” C. H. Bennett, Sci. Am. November, 1987. “The Conversion of Chemical Energy,” D. J. Wink, J. Chem. Educ. 69, 109 (1992). “Energy Conversion,” P. Berdahl, Encyclopedia of Applied Physics, Trigg, G. L., Ed., VCH Publishers, New York (1993), Vol. 6, p. 229. “Steam Engines,” S. Luchter, Encyclopedia of Applied Physics, Trigg, G. L. Ed., VCH Publishers, New York (1997), Vol. 19, p. 563. The Third Law of Thermodynamics and Residual Entropy “Ice,” L. K. Runnels, Sci. Am. December 1966. “The Third Law of Thermodynamics and the Residual Entropy of Ice,” M. M. Julian, F. H. Stillinger, and R. R. Festa, J. Chem. Educ. 60, 65 (1983). “How Thermodynamic Data and Equilibrium Constants Changed When the Standard- State Pressure Became 1 Bar,” R. S. Treptow, J. Chem. Educ. 76, 212 (1999). Problems - I ~ . Probability 5.1 Determine the probability that all the molecules of a gas will be found in one half of a container when the gas consists of (a) 1 molecule, (b) 20 molecules, and (c) 2 million molecules. 5.2 Suppose that your friend told you of the following extraordinary event. A block of metal weighing 500 g was seen rising spontaneously from the table on which it was resting to a height of 1.00 cm above the table. He stated that the metal had absorbed thermal energy from the table that was then used to raise itself against gravitational pull. (a) Does this process violate the first law of thermodynamics? (b) How about the second law? Assume that the room temperature was 298 K and that the table was large enough that its temperature was unaffected by this transfer of energy. (Hint: First calculate the decrease in entropy as a result of this process and then estimate the probability for the occurrence of such a process. The acceleration due to gravity is 9.81 m s‘ .) The Carnot Heat Engine 5.3 Compare the generation of electricity by a hydroelectric plant to the use of a heat engine. Which method is more efficient? Why? 5.4 Convert the P—Vdiagram for the Carnot cycle to a T—S diagram. What is the area of the enclosed portion? 5.5 The internal engine of a 1200-kg car is designed to run on octane (Cngg), whose enthalpy of combustion is 5510 k] mol‘l. If the car is moving up a slope, calculate the maximum height (in meters) to which the car can be driven on 1.0 gallon of the fuel. Assume that the engine cylinder temperature is 2200 °C and the exit temperature is 760 °C, and neglect all forms of friction. The mass of 1 gallon of fuel is 3.1 kg. [Hint The work done in moving the car over a vertical distance is mgh, where m is the mass of the car in kg, 9 the acceleration due to gravity (9.81 m 5’2), and h the height in meters] . 5.6 A heat engine operates between 210 °C and 35 °C. Calculate the minimum amount of heat that must be withdrawn from the hot source to obtain 2000 J of work. 159 160 Chapter 5: The Second Law of Thermodynamics The Second Law of Thermodynamics 5.7 Comment on the statement: “Even thinking about entropy increases its value in the universef’ 5.8 One of the many statements of the second law of thermodynamics is: Heat cannot flow from a colder body to a warmer one without external aid. Assume two systems, 1 and 2, at T1 and T2 (T2 > T1). Show that if a quantity of heat q did flow spontaneously from 1 to 2, the process would result in a decrease 1n entropy of the universe (You may assume that the heat flows very slowly so that the process can be regarded as reversible. Assume also that the loss of heat by system 1 and the gain of heat by system 2 do not affect T1 and T2. ) 5.9 A ship sailing 1n the Indian Ocean takes the warmer surface water at 32 °C to run a heat engine that powers the ship and discharges the used water back to the surface of the sea. Does this scheme violate the second law of thermodynamics? If so, what change would you make to make it work? 5.10 Molecules of a gas at any temperature T above the absolute zero are in constant motion. Does this “perpetual motion” violate the laws of thermodynamics? 5.11 According to the second law of thermodynamics, the entropy of an irreversible process in an isolated system must always 1ncrease. On the other hand, it is well known that the entropy of living systems remains small. (For example, the synthesis of highly complex protein molecules from individual amino acids 1s a process that leads to a decrease 1n entropy.) Is the second law invalid for living systems? Explain. 5.12 On a hot summer day, a person tries to cool himself by opening the door of a refrigerator. Is this a wise action, thermodynamically speaking? 1 (' Entropy Changes 5.13 The molar heat of vaporization of ethanol is 39.3 H mol’l, and the boiling point of ethanol is 78.3 °C. Calculate the value of AvapS for the vaporization of 0.50 mole of ethanol. 5.14 Calculate the values of AU, AH, and AS for the following process: 1 mole of liquid water 1 mole of steam at 25°C and 1 atm —> at 100°C and 1 atm The molar heat of vaporization of water at 373 K is 40.79 kJ mol‘l, and the molar heat capacity of water is 75.3 J K‘1 mol“. Assume the molar heat capacity to be temperature independent and ideal-gas behavior. 5.15 Calculate the value of AS in heating 3.5 moles of a monatomic ideal gas from 50 °C to 77 °C at constant pressure. 5.16 A quantity of 6.0 moles of an ideal gas is reversibly heated at constant volume from 17 °C to 35 °C. Calculate the entropy change. What would be the value of AS if the heating were carried out irreversibly? 5.17 One mole of an ideal gas is first, heated at constant pressure from T to 3T and second, cooled back to T at constant volume. (a) Derive an expression for AS for the overall process. (b) Show that the overall process is equivalent to an isothermal expansion of the gas at T from V to 3V, where Vis the original volume. (c) Show that the value of AS for the process in (a) 1s the same as that for (b). 5.18 A quantity of 35.0 g of water at 25.0 °C (called A) is mixed with 160.0 g of water at 86.0 °C (called B). (a) Calculate the final temperature of the system, assuming that the mixing is carried out adiabatically. (b) Calculate the entropy change of A, B, and the entire system. 5.19 The heat capacity of chlorine gas is given by 5,. = (31.0 + 0.008T) J K-1 mol‘l Problems Calculate the entropy change when 2 moles of gas are heated from 300 K to 400 K at constant pressure. 5.20 A sample of neon (Ne) gas initially at 20 °C and 1.0 atm is expanded from 1.2 L to 2.6 L and simultaneously heated to 40 °C. Calculate the entropy change for the process. 5.21 One of the early experiments in the development of the atomic bomb was to demonstrate that 235U and not 238U is the fissionable isotope. A mass spectrometer was employed to separate 235UF5 from 238UF6. Calculate the value of AS for the separation of 100 mg of the mixture of gas, given that the natural abundances of 235U and 238U are 0.72% and 99.28%, respectively, and that of 19F is 100%. 5.22 One mole of an ideal gas at 298 K expands isothermally from 1.0 L to 2.0 L (a) reversibly and (b) against a constant external pressure of 12.2 atm. Calculate the values of ASSyS, ASsm, and AS“;v in both cases. Are your results consistent with the nature of the processes? 5.23 The absolute molar entropies of 02 and N2 and 205 J K‘1 mol‘1 and 192 J K‘1 mol“, respectively, at 25 °C. What is the entropy of a mixture made up of 2.4 moles of 02 and 9.2 moles of N2 at the same temperature and pressure? 5.24 A quantity of 0.54 mole of steam initially at 350°C and 2.4 atm undergoes a cyclic process for which q = ~74 J. Calculate the value of AS for the process. 5.25 Predict whether the entropy change is positive or negative for each of the following reactions at 298 K: (a) 4FC(S) + 302(9) -> 2F6203(S) (b) 0(g)+0(9) -+ 02(9) (c) NH4C1(s) —> NH3(g) + HCl(g) . ((1) H201) +C12(g) -> 2HC1(9) 5.26 Use the data in Appendix B to calculate the values of ArS° of the reactions listed in the previous problem. 5.27 A quantity of 0.35 mole of an ideal gas initially at 156°C is expanded from 1.2 L to 7.4 L. Calculate the values of w, q, AU, and AS if the process is carried out (a) isothermally and reversibly, and (b) isothermally and irreversibly against an external pressure of 1.0 atm. 5.28 One mole of an ideal gas is isothermally expanded from 5.0 L to 10 L at 300 K. Compare the entropy changes for the system, surroundings, and the universe if the process is carried out (a) reversibly, and (b) irreversibly against an external pressure of 2.0 atm. 5.29 The heat capacity of hydrogen may be represented by 6,. = (1.554 + 0.0022T) J K'1 mol-l Calculate the entropy changes for the system, surroundings, and the universe for the (a) reversible heating, and (b) irreversible heating of 1.0 mole of hydrogen from 300 K to 600 K. [Hints In (b), assume the surroundings to be at 600 K.] 5.30 Consider the reaction N2(g)+02(g) -> 2N0(g) Calculate the values of AIS° for the reaction mixture, surroundings, and the universe at 298 K. Why is your result reassuring to Earth’s inhabitants? 161 162 Chapter 5: The Second Law of Thermodynamics The Third Law of Thermodynamics and Residual Entropy 5.31 The AfFI" values can be negative, zero, or positive, but the S° values can be only zero or positive. Explain. 5.32 Choose the substance with the greater molar entropy in each of the following pairs: (a) H20(l), H20(g), (b) NaCl(s), CaClz(s), (c) N2 (0.1 atm), N2 (1 atm), (d) C (diamond), C (graphite), (e) 02(9), 03 (9), (1') 63131101 (CzHSOH), dimethly ether (C2H60), (g) N204(g), 2N02(9), (h) Fe(s) at 298 K, Fe(s) at 398 K. (Unless otherwise stated, assume the temperature is 298 K.) 5.33 A chemist ft’mnd a discrepancy between the third law entropy and the calculated entropy from statistical thermodynamics for a compound. (a) Which value is larger? (b) Suggest two reasons that may give rise to this discrepancy. . 5.34 Calculate the molar residual entropy of a solid in which the molecules can adopt (a) three, (b) four, and (c) five orientations of equal energy at absolute zero. 5.35 Account for the measured residual entropy of 10.1 J K‘1 mol‘l for the CH3D molecule. 5.36 Explain why the value of S" (graphite) is greater than that of S° (diamond) at 298 K (see Appendix B). Would this inequality hold at 0 K? Additional Problems 5.37 Entropy has sometimes been described at “time’s arrow” because it is the property that determines the forward direction of time. Explain. 5.38 State the condition(s) under which the following equations can be applied: (a) AS = AH / T , (b) S0 = 0, (c) dS = deT/ T, ((1) d8 = dq/T. 5.39 Without referring to any table, predict whether the entropy change is positive, nearly zero, or negative for each of the following reactions: ' (a) N2(g)+02(g) -’ 2N0(9) (b) . 2Mg(S) +02(g) —> 2Mg0(S) (c) 2H202(1) 9 2H200) +0201) (‘1) H2(g)+C02(9) —’ H20(g)+C0(9) 5.40 Calculate the entropy change when neon at 25 °C and 1.0 atm in a container of volume 0.780 L is allowed to expand to 1.25 L and is simultaneously heated to 85 °C. Assume ideal behavior. (Hint: Because S is a state function, you can first calculate the value of AS for expansion and then calculate the value of AS for heating at constant final volume.) 5.41 Photosynthesis makes use of photons of visible light to bring about chemical changes. Explain why heat energy in the form of infrared photons is ineffective for photosynthesis. 5.42 One mole of an ideal monatomic gas is compressed from 2.0 atm to 6.0 atm while being cooled from 400 K to 300 K. Calculate the values of AU, AH, and AS for the process. 5.43 The three laws of thermodynamics are sometimes stated colloquially as follows: First law: You cannot get something for nothing; Second law: The best you can do is get even; Third law: You cannot get even. Provide a scientific basis for each of these statements. (Hint: One consequence of the third law is that it is impossible to attain the absolute zero of temperature.) 5.44 Use the following data to determine the normal boiling point, in kelvins, of mercury. What assumptions must you make to do the calculation? Hg(l): Affi°= 0 (by definition) S°= 77.4 J K"1 mol-l Hg(g): AfH°= 60.78 kJ mol" ' §°= 174.7 J K“ mol-l Problems 5.45 Referring to Trouton’s rule, explain why the ratio is considerably smaller than 90 J K‘1 mol‘1 for liquid HF. 5.46 Give a detailed example of each of the following, with an explanation: (a) a thermodynamically spontaneous process; (b) a process that would violate the first law of thermodynamics; (c) a process that would violate the second law of thermodynamics; (d) an irreversible process; (e) an equilibrium process. i’ 5.47 In the reversible adiabatic expansion of an ideal gas, there are two contributions to entropy changes: the expansion of the gas and the cooling of the gas. Show that these two contributions are equal in magnitude but opposite in sign. Show also that for an irreversible adiabatic gas expansion, these two contributions are no longer equal in magnitude. Predict the sign of AS. 5.48 A refrigerator set at 0 °C discharges heat into the kitchen at 20 °C. (a) How much work would be required to freeze 500 mL of water (about an ice tray’s volume)? (b) How much heat would be discharged during this process? (The molar enthalpy of fusion of water is 6.01 k] mol‘l, and the refrigerator operates at 35% efliciency.) 5.49 Superheated water is water heated above 100 °C without boiling. As for supercooled water (see Example 5.7), superheated water is thermodynamically unstable». Calculate the values of ASsys, A551,", and AS“,v when 1.5 moles of superheated water at 110 °C and 1.0 atm are converted to steam at the same temperature and pressure. (The molar enthalpy of vaporization of water is 40‘. 79 kJ mol‘l, and the molar heat capacities of water and steam in the temperature range 100—110°C are 75.5 J K‘1 mol‘1 and 34.4 J K‘1 mol‘l, respectively. 5.50 Toluene (C7H3) has a dipole moment, whereas benzene (C5H5) is nonpolar: CH3? m.pt. 5.5°C —95°C b.pt. 80.1°C 110.6°C Explain why, contrary to our expectation, benzene melts at a much higher temperature than toluene. Why is the boiling point of toluene higher than that of benzene? 163 ...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern