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1 CBE 141: Chemical Engineering Thermodynamics, Spring 2018, UC Berkeley Midterm 2 March 22, 2018 Time: 80 minutes, closed-book and closed-notes, one-sided 8 ½ x 11 equation sheet allowed Please show all work and clearly mark your answers. Write your name on any additional pages of scratch work. You must turn in your equation sheet with your exam. Point Totals: Problem Problem 7 20 Problem 8 30 Problem 9 20 Problem Extra credit 10b 5 Problem Extra credit Total (points) 137 Total (percentage) 100 This exam has 14 pages and 12 questions 1

2 Problem 1 (6 points) A turbine cannot be run with 100% efficiency due to a variety of losses, one of which includes friction at the upstream nozzle which reduces the available fluid enthalpy coming into the turbine. Which of the following is a consequence of this non-ideality? You may circle more than one, or none at all. A. The friction of the fluid in the nozzle increases the enthalpy available to the turbine B. The friction of the fluid in the nozzle reduces the enthalpy available to the turbine C. The velocity leaving the nozzle is less than the velocity calculated with isentropic expansion. D. The velocity leaving the nozzle is more than the velocity calculated with isentropic expansion. E. The flow coming into the turbine can be considered isothermal F. The flow coming into the turbine can be considered isentropic Problem 2 (5 points) When comparing the Otto and Diesel cycles, which of the following are true? You may circle more than one, or none at all. A. Otto cycle has higher efficiency for the same maximum (i.e. compression) pressure B. Otto cycle has higher efficiency for the same compression ratio C. The area enclosed by the Diesel cycle on a PV diagram (i.e. Work) is larger than the area enclosed by a real compression engine. D. The area enclosed by the Otto cycle on a PV diagram (i.e. Work) is larger than the area enclosed by a real spark-ignition engine. E. The largest contributor to non-ideality (i.e. inefficiency) of running an Otto or Diesel cycle is ignoring the intake and exhaust strokes. Problem 3 (5 points) Consider the following exact differential: dh = TdS + VdP, which of the following is INCORRECT: a. ) *+ *, -. = T d. )*. */ - 0 = )*, *0 -. b. ) *+ *. -, = V e. ) */ *. -, = )*0 *, -. c. ) */ *. -, = *1 + *,*. 2

3 Problem 4: (5 points) Which will have the highest magnitude for the residual enthalpy (H R ) at 100 o C? The vapor pressure of water at 100 o C is 1 bar. A. Water at 2.0 bar B. Water at 0.5 bar C. Argon at 2.0 bar D. Argon at 0.5 bar E. Not enough information Problem 5 (5 points) Which of the following statements are true regarding an ideal gas mixing process. You may circle one, more than one, or none at all: A. Mixing is always a spontaneous process B. Enthalpy of mixing must be greater than zero C. Entropy of mixing must be greater than zero D. The change in entropy during a mixing is not temperature dependent E. A 50/50 binary mixture will achieve the highest change in entropy when mixed 3

4 Problem 6 (6 points) Label the on the given Txy graph of benzene and toluene at 1atm and an initial composition of z = 0.40 (3 points): A. Superheated vapor region B. Dew point C. Bubble point and calculate the vapor/liquid compositions and relative compositions of the vapor and liquid phases if a mixture with an initial composition of z = 0.40 at 75 C is heated to 100 C (3 points). 4

5 Problem 7 (20 points) Consider the following ideal Vapor-Compression cycle: Starting with the first law energy balance and second law entropy balance, prove that the maximum value of the coefficient of performance for a refrigeration cycle is equal to the following expression: 5

6 Problem 8 (30 points) A diesel cycle has a compression ratio of 18 and a cutoff ratio of 2.5. Initially (at state 1), the state is fixed by a pressure of 0.9 bar, and a temperature of 300 K. a) What are the temperatures of the states, with the initial state as state 1, following an isentropic compression to T 2, an isobaric heat addition to T 3, and an isentropic expansion to T 4. (30 points) b) Extra Credit What is the thermal efficiency of the cycle? You may assume Cp = kj/kg K and Cp/Cv = 1.4 for the working fluid. (5 points no partial credit) 6

7 Problem 9 (20 points) Using the ideal gas equation of state (PV=RT), calculate the three partial derivatives that appear in the triple product rule between P, T, and V. Hint: Show that their product equals -1. 7

8 Problem 10 (15 points) Pure ethanol boils at a temperature of 63.5 ºC at a pressure of 400 torr. It also boils at 78.4 ºC and 760 torr. a) What is the enthalpy of vaporization of pure ethanol? (15 points) b) Extra credit: Estimate the saturation pressure for ethanol at 100 ºC. (5 points no partial credit) 8

9 Problem 11 (20 points) Consider a mixture of chemical species 1 and 2. Below is a plot of partial molar volumes in cm 3 /mol for both species (V3 2 and V555) 4 with respect to x 1. For a mixture of 2 mol of species 1 and 3 mole of species 2, determine the following (approximate values based on interpretations of the graph above are okay): a) Total molar volume, V b) Pure component molar volumes, V 1 and V 1 c) Molar volume of an ideal mixture of 2 mol species 1 and 3 mol species 2 9

10 EXTRA CREDIT Q 12 (10 points final answer must be correct, no partial credit!): What is the residual volume in the ideal gas state? Hint: Show that simultaneously applying both ideal gas limits of P à 0 and Z à 1 yields an indeterminate (i.e. 0 0). Hint: Calculate the ratio of V R /V as a function of Z. 10

11 Additional space provided for work. 11

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13 Additional space provided for work. 13