Hw2 solutions PCHEM

Hw2 solutions PCHEM - CHEM131 Homework n°2 1. Levine 2.1...

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Unformatted text preview: CHEM131 Homework n°2 1. Levine 2.1 a. The kinetic energy of a system of several particles equals the sum of the kinetic energies of the individual particles. True b. The potential energy of a system of interacting particles equals the sum of the potential energies of the individual particles. False 2. Levine 2.13 a. For every process, ∆Esyst = -∆Esurr. - True For any process: ∆Esyst + ∆Esurr = 0 b. For every cyclic process, the final state of the system is the same as the initial state. - True c. For every cyclic process, the final state of the surroundings is the same as the initial state of the surroundings. - False. Final and initial states refer only to the system and not to the surroundings. d. For a closed system at rest with no fields present, the sum q + w has the same value for every process that goes from a given state 1 to a given state 2. - True. The sum of q + w = ∆U, that is a state function of the system. e. If systems A and B each consist of pure liquid water at 1 bar pressure and if TA > TB, then the internal energy of system A must be greater than that of B. - False. ∆U= q + w 3. Levine 2.24 a. The quantities H, U, PV, ∆H, and P∆V all have the same dimensions. - True. All of them have the same dimensions: work (energy) b. ∆H is defined only for a constant- pressure process. - False. It can also be defined for constant- volume process for condensed phases at moderate pressures. c. For a constant- volume process in a closed system, ∆H= ∆U - False. ∆H= ∆U for condensed phases not at high pressures. 4. Levine 2.42 a. A thermodynamic process is defined by the final state and the initial state. - False. A thermodynamic process is defined by series of thermodynamic states through which the system passes on its way from the initial state to the final state. b. ∆T =0 for every isothermal process. - True. In an isothermal process, T is constant throughout the process; therefore ∆T =0. c. Every process that has ∆T =0 is an isothermal process. - False. ∆T =0 can also occur in cyclic process. d. ∆U=0 for a reversible phase change at constant T and P. - False. ∆U= q + w for a reversible phase change. e. q must be zero for an isothermal process. - False. q ≠ 0 in an isothermal process. f. ∆T must be zero for an adiabatic process. - False. q = 0 but not ∆T. 5. Levine 2.45 a. Reversible melting of solid benzene at 1 atm and the normal meting point. b. Reversible melting of ice at 1 atm and 0°C. c. Reversible adiabatic expansion of a perfect gas. d. Reversible isothermal expansion of a perfect gas. e. Adiabatic expansion of a perfect gas into a vacuum (Joule experiment). f. Joule- Thomson adiabatic throttling of a perfect gas. g. Reversible heating of a perfect gas at constant P. h. Reversible cooling of a perfect gas at constant V. q w ∆U a. + + b. + + + c. 0 d. + 0 e. 0 0 0 f. 0 0 0 g. + + h. 0 - ∆H + + 0 0 0 + - 6. Levine 2.67. A student attempting to remember a certain formula comes up with C p- Cv = TVαm/κn, where m and n are certain integers whose values the student has forgotten and where the remaining symbols have their usual meanings. Use dimensional considerations to find m and n. Cp- Cv = TVαm/κn , where m and n are integers. Dimensions of the physical quantities: The powers of temperature in each side of the equation are: For n, So the powers of energy in each side of the equation are: 7. A sample consisting of 2.0 mol of a monoatomic perfect gas, for which Cv,m= 3R/2, initially at P1= 1.50 atm and T1= 300K is heated reversibly to 400K at constant volume. Calculate the final pressure, ∆U, q, and w. a. Final pressure b. ∆U c. Work, w d. Heat, q 8. A sample of argon mass of 6.56g occupies 18.5L at 305K. a. Calculate the wo rk done when the gas expands isothermally against a constant external pressure of 7.7 kPa until its volume is increased by 3.5L. b. Calculate the work that would be done if the same expansion occurs reversibly. a. Isothermal expansion a constant external pressure b. Work when the expansion occurs reversible. 9. Consider a perfect gas contained in a cylinder and separated by a frictionless adiabatic piston into two sections, A and B; section B is in contact with a water bath that maintains it at constant temperature. Initially TA = TB = 300 K, VA = VB =2.00 L, and nA = nB = 3.00 mol. Heat is supplied to Section A and the piston moves to the right reversibly until the final volume of Section B is 1.00 L. Calculate (a) the work done by the gas in Section A, (b) ΔU for the gas in Section B, (c) q for the gas in B, (d) ΔU for the gas in A, and (e) q for the gas in A. Assume CV,m = 25.0 J K−1 mol−1. a. Work done by the gas in section A b. ΔU for the gas in Section B c. q for gas in B. d. ΔU for the gas in A e. q for the gas in A. 10. Let z = x/(1 + y2). Find dz. 11. Determine whether or not dz = xydx + xydy is exact by integrating it around the closed curve formed by the paths y = x and y = x2 between the points (0, 0) and (1, 1). Note: while there are other ways to determine whether dz is exact, want you to do it this particular way. 1. x= y 2. y= x2 Since each path gives different results; dz in not an exact differential. ...
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This note was uploaded on 02/07/2011 for the course CHEM 131 taught by Professor Lindenberg during the Spring '08 term at UCSD.

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