Practice Examinations Chem 393 Fall 2005 Time 1 hr 15 min for each set.

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1 Practice Examinations Chem 393 Fall 2005 Time 1 hr 15 min for each set. The symbols used here are as discussed in the class. Use scratch paper as needed. Do not give more than one answer for any question. It will automatically disqualify both answers. [R = J/Kmol; 1 atm = 101.3kPa] Name:

2 Exam I 1. Derive the thermometric equation for the centigrade scale, in terms of gas pressure. 4. What is the heat produced when a gas is compressed, under isothermal conditions, from its initial state p1, V1, T1 to a final state, p2, V2, T1? Consider it to be one-step compression by an external pressure, which is twice the final pressure. 2. Show that the pressure exerted by a liquid column is a product of its density, height of the column and acceleration due to gravity? 5. Indicate if the following statements are true or false: 3. If a gas has a density ρ at pressure p, what is its root mean square velocity in terms of density and pressure? a. Melting of ice at zero degrees centigrade, 1 atm (in equilibrium with liquid water) is a reversible process. [ ] b. Energy is neither created nor destroyed. [ ] c. The coefficient of volume expansion for a gas is negative. [ ] d. Perpetual motion machine of the second kind is possible.

3 6. Show that p = ρ RT/M, starting from the ideal gas law. 9. Plot p versus V, for an isothermal, reversible expansion of an ideal gas. 7. Use the expression for pv = (1/3) Nm<c 2 > (kinetic theory of gases) and show that the internal energy of the gas is (3/2) nrt. 10. Plot pressure versus height, at constant T, for oxygen and nitrogen gases. 8. Derive an expression for the work done during single step isothermal, reversible expansion of an ideal gas.

4 11. Starting from the second law of thermodynamics, show that S = Cp ln(t2/t1) for an ideal gas, at constant pressure. 13. Plot S vs T for Carnot cycle (4 step, reversible cycle)? 14. Plot entropy vs pressure of an ideal gas. 12. Show that the work done in an adiabatic expansion of an ideal gas is equal to change in its internal energy. 15. Plot H vs T for the Carnot cycle.?

5 Practice Exam II: 1. Show that TdS = du + pdv, starting from the first and the second laws? 3. What is the entropy change when 1 mol of ice melts to water at 0 C, and 1 atm? Heat of fusion of water is 22 J/Kmol. 2. What is the entropy change due to isothermal expansion of 1 mol of an ideal gas such that the volume doubles. 4. What is the number of possible distinguishable arrangements of five identical objects in seven boxes (single occupancy in each box)?

6 5. If change in the internal energy when one mol of hydrogen reacts with half a mol of oxygen is 250 kcal, at 300 K, what is the corresponding enthalpy change? 7. One mol of a gas is heated at constant volume from 300K to 500K. If Cv for one mol of the gas is (3/2)R, calculate the entropy change for this process. 9. Show that TdS = du + pdv (constant pressure, pv work only) 6. Cp of solid silver is T in units of J/Kmol. Calculate H when 3 mol of silver is heated from 25 C to its melting point, 961 C, at 1 atm. 10. Show that ds> dqirr/t for all irreversible processes (Clausius inequality)

7 11. Show that q for a constant volume process is a state function. 14. A. The entropy change accompanying an isothermal expansion of 1 mol of ideal gas when the volume doubles is a. Rln2 b. 1/12 x R c. -ln2 d. Rln1/2 e.none of these B. The efficiency of a cyclic engine operating between 200 K and 300 K is a b c. 1/3 d. -1/3 e. 1/2 C. The efficiencies of a steam engine (high t = 100 C) in summer time (when the lower t is at 20 C) and in winter time (when the lower T is at -20 C) are a. 0.5 and 0.4 b and 0.67 c and 0.54 d and 0.32 D. The entropy change when 1 mol of ice melts to water at 273 K, 1 atm is 22 J K -1 mol -1. The molar enthalpy change of water is a. 22 x 273 J/mol b. -22 x 273 J/mol c. 22/273 J/mol d.-22/273 J/mol. 12. Graph S vs p for an ideal gas, constant T. 15. Plot G mixing as a function of mole fraction of a component in a binary mixture. 13. Plot entropy vs p for an adiabatic reversible expansion.

8 Practice Exam III (some questions are bit more advanced) 1. Draw the phase diagram of any substance other than water at the region of the triple point. 4. Show that d(g/t)/dt = - H/T 2 at constant pressure. 2. Plot chemical potential of a solid phase as a function of temperature. 5. Show that: dh = TdS + Vdp 3. Show that dg=vdp - SdT.?

9 8. What is the change in temperature in the above process? 6. Show µ = µ + RT ln p. 7. Calculate the change in volume when 1 mol of hydrogen at 1 atm and 25 C is mixed with 2 mol of nitrogen at 1 atm and 25 C. Assume ideal mixture. 9. What is G when 2 mol of hydrogen is mixed with 1 mol of carbon dioxide at 300 K? Chemical potentials of these substances are 2 and 3 kj/mol, respectively, at 300 K. 10. What is A when 1 mol of hydrogen reacts with 2 mol of oxygen, if the reaction is carried out at constant temperature and constant volume?

10 13. Show that the work done in an isothermal reversible expansion of an ideal gas is - p 2 V 2 ln(v 2 /V 1 ). 11. Indicate if the following statements are true or false a. Gibbs free energy increases during any chemical reaction. b. Entropy of the universe is increasing with time. 14. Show that work done in an irreversible cyclic transformation is >0. c. All exothermic reactions are spontaneous processes. d. Free energy decreases during any spontaneous process. e. For an ideal mixture, the Gibbs free energy of mixing is zero. f. The Gibbs free energy of an ideal gas decreases with increase in pressure. 12. Show that w is a path function. 15. Derive an expression for the work done by an ideal gas during a reversible isothermal expansion.

11 3. Plot enthalpy vs p for an isothermal reversible expansion for an ideal gas. Some additional questions: 1. Derive an expression for the work done by an ideal gas due to an isothermal irreversible expansion against an opposing pressure. 4. A. S when 24 mg of N2 at 89 torr and 22 C expands adiabatically into vacuum to a final pressure of 34 torr, S is (assume perfect gas behavior). a. 8.7 J/K b. 27 mj/k c. 1.2 J/K d. 6.9 mj/k B. S for the melting of 5.0 g of ice (fusion enthalpy is 79.7 cal/g) at 0 C and 1 atm is a cal/k b. 1.2 cal/k c cal/k d J/K C. The entropy change when an ideal gas (1 mol) undergoes free expansion (into vaccum) at 300 K is a. >0 b. <0 c. =0 d. e. None of these D. Melting of a solid in equilibrium with its liquid is a reversible process a. false b. true c. may be d. none of these More Questions 2. Show that the magnitude of work done in a two step isothermal expansion is more than a single step isothermal expansion (same initial and final states). 1. Graph S vs T for an ideal gas, constant V. 2. Plot entropy vs volume, ideal gas at constant T. 3. Graph S vs U for an ideal gas, constant V. 4. Plot p vs V for Carnot cycle. 5. Plot ε vs 1/T 2 for the above cycle. 6. Plot H vs T for the above cycle. 7. Graph U vs T for a reversible cycle consisting of two expansion and two compression steps (Carnot Cycle). 8. Plot p vs V for the above cycle. 9. What will be W cycle if the two temperatures of the above cycle are equal? 10. Graph q p vs T at constant pressure for an ideal gas. 11. Graph Cp vs T for an ideal gas. 12. Graph T vs p for an isoenthalpic/adiabatic expansion of an ideal gas.

12 13. Graph work done in an isothermal reversible expansion as a function of temperature for an ideal gas. 14. Graph the same as above but for an irreversible expansion. 15. Graph q vs T for an ideal gas at constant volume (Cv is a constant). 16. Graph work done in an isothermal reversible expansion as a function of increasing initial pressure for an ideal gas. 17. Show that du = C v dt for an ideal gas. 18. Graph U vs T for an ideal gas, constant V. Indicate Cv. 19. Graph q vs T for the heating of ice from 263 K to 283 K at atm. pressure (assume Cp of water and Cp of ice are constants). 20. Graph work done during one-step isothermal compressiondue to an external pressure of p ext. 21. Graph work done during isothermal reversible expansion of an ideal gas. 22. Graph the work done in two-step isothermal expansion of a gas. 23. A. The work done during the one-step isothermal expansion of a gas against constant external pressure (P ex ) is a. P ex xchange in Volume b. - P ex xchange in Volume c.0 d. unknown B. The magnitude of work done during a reversible isothermal expansion of an ideal gas (W rev ) is related to the corresponding work done during an irreversible expansion (W irr ) as a. W rev < W irr b. W rev = W irr c. W rev > W irr d. W irr =0 C. The work done by an ideal gas (1mol) during an isothermal expansion into vacuum with a change in volume equal to 25 lit. at 300 K is a. 25 lit atm b. >25 lit atm c. 0 d. <0 e. None of these D. Total entropy change S (system + surroundings) when an irreversible change occurs in the system is a. <0 b. >0 c. = 0 d. None of these e. 0.5R

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