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Unformatted text preview: ChE 359 Examination Policy
Washington University academic integrity policy
Effective learning, teaching and research all depend upon the ability of members of the academic community to trust one another and to trust the integrity of work that is submitted in classes for academic credit or conducted in the wider arena of scholarly research. When such an atmosphere of mutual trust exists, the free exchange of ideas is fostered, and all members of the community are able to work to achieve their highest potential. In all academic work, it is important that the ideas and contributions of others be appropriately acknowledged, and that work that is presented as original is in fact original. Ensuring the honesty and fairness of the intellectual environment at Washington University is a responsibility that is shared by faculty, students, and administrative staff. In the event of an academic violation, the instructors may exercise their right to report the student(s) in question to the Discipline Committee of the School of Engineering and Applied Science. Examination pledge
Please write out the following statement, sign, and date. "I have neither given nor received aid on this examination, nor have I concealed a violation of the academic integrity policy.” Name (printed) Student ID number Signature Date ChE 359 Exam #1
Tuesday, February 9, 2010
1. (45 points) The function of cells and tissues is often governed by the mechanical stresses on proteins, polysaccharides, and DNA. To study these functions, engineers often use atomic force microscopy, which is a single-molecule measurement technique, to stretch these biomolecules under physiological (i.e., aqueous) conditions. In this problem, a single protein molecule (titin)i is being stretched at constant temperature between the tip of a microscopic cantilever and a flat, goldcovered substrate. The pressure of the environment is kept constant. The forces acting on the molecule as it is extended are transmitted to the cantilever, and a force vs. extension curve is generated. a. (10 points) Identify the system in the stretching process, and state the natural/independent variables that are measured/controlled at the system boundary. b. (5 points) Write the fundamental energy equation corresponding to this system. c. (5 points) Given the natural variables from part a., write the fundamental equation corresponding to these variables. d. (10 points) Derive a Maxwell relation for calculating the change in entropy in the protein as a function of its length, in terms of measurable properties of the system. Use this to calculate the total entropy change during the stretching process. e. (10 points) Given that a typical force-extension curve for the stretching of titin is shown to the right, explain qualitatively how the entropy changes (e.g., increases, decreases, or stays the same) during the stretching process. f. (5 points) Comment on what is happening to the system to produce the sawtoothed pattern in the force-extension curve at 200 pN. 2. (55 points) One proposed method of carbon dioxide sequestration involves enhanced oil recovery, where a fixed amount of carbon dioxide is injected into an Page 1 of 2 ChE 359 SP2010 – Exam #1 oil reservoir. The reservoir walls are fixed in size and kept at a constant temperature. During the sequestration process, carbon dioxide expands irreversibly into the rest of the reservoir. The result is that the oil is pushed up from the reservoir into the production well. a. (10 points) Identify the system in the expansion process, and state the natural/independent variables that are measured/controlled at the system boundary. b. (5 points) Given the natural variables from part a., write the fundamental equation corresponding to these variables. c. (15 points) For this problem, assume that carbon dioxide can be treated as an ideal gas. Derive a Maxwell relation for the change in entropy during the expansion process. Use this relation to derive an expression for the change in internal energy during the expansion process. d. (10 points) State whether work is being done on or by the system during the expansion, and justify your choice. State the implications for heat flow to or from the system. e. (15 points) At high temperatures and pressures, carbon dioxide is a supercritical fluid, which, instead of being described by the ideal gas law, 2 NRT a(T ) N is described by the Peng-Robinson equation of state: P = , − V −b V2 where a(T ) is a function of temperature and b is a positive constant. Based on your answer to part d., derive an expression for the change in internal energy during the expansion process, and comment on how it € differs from that calculated using the ideal gas description. € € i Journal of Structural Biology 137, 194–205 (2002) Page 2 of 2 ...
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