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AnswerKey_Quiz_4_Fall2008 - Quiz#4 Chem 3615 Physical...

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Unformatted text preview: Quiz #4 Chem 3615- Physical Chemistry Instructor: Esker September 15, 2008 NAME:_____Answer Key________ Score = 40 + _______x15 = _______ Useful Information: pV = nRT, R = 8.314 Jmol-1K-1 = 0.08206 Latmmol-1K-1, 1 atm = 760 mm Hg = 760 Torr = 101325 Pa, 0.001 m3 = 1 L = 1000 cm3, dW = - Fdz = -popdV, Euler's Formula x y z 1 V 1 V nRT an 2 , dU = dQ + dW, H = U + pV, = -1 , p = , = - , =- y z (V - nb ) V 2 V p T V T p z x x y T U H -1 CV = = constant, pV = constant, p1- T = , Cp = , JT = , dS = dQ/T, TV p T V T p H constant, = Cp/Cv, G = H-TS, A = U-TS Circle the correct letter. If you change your mind, make sure the original answer is completely erased. If you are using a pen, black out a wrong answer completely 1. Consider the following equation of state where a > 0 and constant: Indicate which of the following statements must be true or that all of the above are false for this equation of state. (a) A temperature exists where Z > 1 (c) The coefficient of thermal expansion is 1/T (e) All of the above are false (b) The gas has a Boyle temperature (d) The isothermal compressibility is 1/p From the expression for Z, we see that Z is independent of p. It's value is always < 1 and only approaches 1 in the limit of infinite temperature. For these reasons: (a) False, Z < 1 at all T (b) False, as Z only approaches 1 in the limit of infinite temperature and is otherwise < 1. (c) (d) , Notice that while a perfect gas must yield , does not mean the gas is perfect!!!! Page 1 of 3 2. Which of the following statements is true about total differential (I) and (II)? 1 (a) Only I is exact (d) Neither I nor II is exact ? & (c) Both I & II are exact (b) Only II is exact (e) None of the above statements is correct ? , ? ? , 3. Two moles of an ideal diatomic gas at 5000K (high enough temperature that all vibrational modes are active) is compressed isothermally and reversibly from 2.00 m3 to 1.00 m3. What is W for the process? (a) -83.1 kJ (b) -57.6 kJ (c) -28.8 kJ (d) 28.8 kJ (e) 57.6 kJ . . . , . Page 2 of 3 4. A mole of an ideal monatomic gas is heated isometrically (isochorically) from an initial volume and temperture of 0.250 m3 and 300 K (State A), respectively, to twice its original temperature (State B). The gas is then expanded isobarically to twice its molar volume (State C). The gas is then cooled to its original temperature isometrically (isochorically) (State D). In the final step, the gas returns to the initial state isothermally and reversibly (State A). Indicate which of the following statements could be correct or that all of them are incorrect. Hint: While you can solve this mathematically, drawing an appropriate graph should make this unnecessary. (a) The pressure at C is less than the pressure at A. False, see figure. (b) The complete cycle is exothermic. False, for this process, Wcycle < 0 (see C). As Ucycle = 0, Qcycle = Wcycle. Since Wcycle < 0, Qcycle > 0. (c) The net work for the complete cycle is negative. True, the area inside the loop ABCDA represents the magnitude of the net work for the cycle. The magnitude is the area under the isobaric step (red) the area under the isothermal step (blue). As the red area is left-over (only 1 diagonal shading) and during B to C, the gas is expanding, i.e. the system is doing work on the surroundings, the work during the expansion is negative (red shading). Hence, Wcycle < 0 (red shading is left over). (d) U going from D to A is larger if we use two moles of gas. False, for an ideal gas, U is only a function of temperature. As dT = 0, U = 0. It does not matter how big the gas molecules are, only that they behave ideally. (e) All of the above are incorrect. Blue shading represents the area under the isothermal compression step (D to A). This area is positive (compression). The red shading represents the area under the isobaric step (C to D). This area is negative (expansion). The net area (inside the cycle) is red (negative). Hence Wcycle < 0. As Ucycle = 0, Qcycle = -Wcycle > 0 (endothermic heat flows into the system). Page 3 of 3 ...
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