3.012 Quiz 1 3.012 10.12.05 Fall 2005 100 points total (50 in thermo + 50 in bonding) Give as much written explanation as possible of your reasoning, and write clearly and legibly. Time yourself carefully – do not spend most of your time on a single question. Remember, you have close to two hours (from 1.05pm to 2.55pm). You can start with thermo, or start with bonding. Write your name here: ___________________________________________ 3.012 Quiz 1 1 of 13 8/25/06Physical Constants: Gas constant: R = 8.3144 J/mole-K = 0.082057 L-atm/mole-K Thermodynamics. (2 problems, 50 points total). 1. Analyzing an isothermal process. Consider the process described schematically below. One mole of an ideal gas is confined in a rigid cylinder in a volume of 1 L by a movable frictionless piston on top; the piston is free to move in response to changes in the system. The system is placed inside a confined heat reservoir, and the combination of the system + the heat reservoir can be considered isolated. The heat reservoir is capable of transferring heat without changing it’s temperature significantly (think of it as a very large water bath). A quantity of 10 kJ of heat transfers from the heat reservoir into the system. During this process, the temperature of the system and heat reservoir are constant at 300K. Answer the questions below about this process. pistonqTsurr = 300 KTsys = 300 KHeat reservoir a. What is the internal energy change in the gas? b. What happens to the piston once the heat is absorbed by the gas? Calculate the work done on the piston, and state whether this is work done on the gas or work done by the gas. c. What is the final state (pressure and volume) of the gas? d. Using the second law, show that this process is reversible. 3.012 Quiz 1 2 of 13 8/25/06WORKSPACE FOR PROBLEM 1:3.012 Quiz 1 3 of 13 8/25/062. The Thermodynamics of nanoparticle-based cancer therapy. Recently, a novel anti-cancer therapy has been developed at Rice University, based on the design of nanomaterials that become rapidly superheated in response to illumination with laser light. The therapy is illustrated below: Amorphous silica nanoparticles with diameters of ~100 nm are coated with a very thin (~10 nm thick) shell of gold. When irradiated by an infrared laser (λ ~ 800 nm), which passes through normal tissues with almost no absorption, the particles absorb the light and efficiently convert it to heat, and thus are rapidly heated to very high temperatures. This heating response is being exploited to kill tumor cells, by injecting the nanoparticles into a tumor (see the figure), and illuminating for a few minutes with an infrared laser. Normal tissues and tumors are at 37°C, but if tumor cells are heated to ~45°C, they are killed. Let’s carry out a simplified thermodynamic analysis of the requirements for this process. Suppose we can approximate a local 1 cm3 region of tumor and healthy tissue to be isolated from the surrounding tissue and environment outside the body. We inject 100 mg of nanoshells into the tissue and irradiate for 60 seconds with the infrared laser. As a first-order approximation, let’s assume the tissue, which is >70% water, is comprised of pure water. All of these processes occur at a constant pressure of 1 atm. Use the physical data for the system given below to answer the following questions: Data for SiO2 (amorphous solid): Molecular weight = 60.1 g/mole ρ= 2.4gcm3 C p,SiO2= 44.5Jmole ⋅ K αSiO2=1.2×10−6K−1 Data for H2O (liquid): Molecular weight = 18 g/mole ρ= 1.0gcm3 C p, H2O= 75.31Jmole ⋅ K 3.012 Quiz 1 4 of 13 8/25/06 Healthy TissueTumorSilica NanoshellsAu Shells(~10 nm diameter)(~100 nm diameter)SiO2 nanoparticleFigure by MIT OCW.the presence of the gold shell for this calculation– consider that the nanoparticles are composed of pure silica. c. Calculate the entropy change in the silica particles during the process of cooling them into thermal equilibrium with the tissue after laser heating. d. Is your result from part (c) in conflict with the second law? Explain why or why not. e. The nanoshells start at 37°C before laser irradiation, and are then heated to the temperature you determined in part (b) by the laser. Will the volume change in the nanoparticles induced by this heating process be more than 1%? Explain your answer with a calculation. (You may neglect the effect of the gold shell and the surrounding tissue for this estimate- consider the nanoparticles are pure silica and can freely expand against the surrounding tissue). [This problem is based on the gold nanoshell phototherapy research of J.L. West and Naomi Halas at Rice University.] 3.012 Quiz 1 5 of 13 8/25/06 a. What is the implication of assuming that the tissue volume + nanoparticles are an isolated system? Explain in 1-2 sentences. b. Suppose that the nanoshells are heated quickly enough that no heat transfer between the particles and tissue occurs until after the laser is turned off, i.e., the nanoshells start at some temperature (clearly, greater than 37°C!) induced by the laser, and then exchange heat with the local tissue to reach thermal equilibrium. In order to heat the 1 cm3 region of tissue from its starting temperature of 37°C to 45°C, to what temperature would the nanoshells need to be initially heated by the laser? NeglectWORKSPACE FOR PROBLEM 2: 3.012 Quiz 1 6 of 13 8/25/06WORKSPACE FOR PROBLEM 2: 3.012 Quiz 1 7 of 13 8/25/06Bonding. (2 problems, 50 points total). 1) Lithium ions [8 questions, a) to h)]: Lithium is the third element of the periodic table (following hydrogen and helium) and it has 3 protons in the nucleus. We’ll discuss in this problem Li++ (i.e. the doubly-ionized lithium ion, with only one electron around the nucleus), Li+ (the singly-ionized lithium, with two electrons around the nucleus), and Li (the neutral ion, with three electrons around the nucleus). a. What is the stationary Schroedinger equation for the single electron in Li++ ? b. What is the ground-state energy for that electron (specify your units) ? c. Determine the wavelength of a photon that is able to excite that electron from the ground state to the first excited state (you can use the International System for the units of measure, given below, or atomic units – in atomic units the speed of
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