Physics 360 Review 3
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1 Physics 360 Review 3 The test will be similar to the second test in that calculators will not be allowed and that the Unit #2 material will be divided into three different parts. There will be one problem from the Unit #1 test and one from the Unit #2 test. Information that will be provided F = U TS, H = U + PV, G = U + PV TS At constant energy and volume, S tends to increase. At constant temperature and volume, F tends to decrease. At constant temperature and pressure, G tends to decrease. Some of the following may be given, but you may be asked to prove them: du = T ds P dv + dn dh = T ds + V dp + dn df = P dv + dn S dt dg = S dt + V dp + dn thermodynamic identities., etc. There are 24 such equations that can be easily derived from the
2 Section I. Review Question (2 problems, 10 points each) Taken from the first two exams. See solutions online. Section II. Qualitative Questions (3 problems, 10 points each) Understand the following basic ideas. Be sure to be able to describe them in terms of concepts as well as in terms of equations. Operation of engines and refrigerators: Be able draw and/or describe Fig. 41. and 4.4. Efficiency: work out/heat in. COP: Heat in (out of cold reservoir) / work Throttling: Forcing a fluid through a porous plug, so it cools as it expands into a region of lower pressure. Helmholtz free energy: Energy needed to create something minus the energy that can be provided by the a thermal reservoir. Gibbs free energy: Energy needed to create something and move gas out of the way minus the energy that can be provided by the a thermal reservoir. Extensive quantities: proportional to number of molecules present. Intensive quantities: independent of number of molecules present. Critical point: P and T at which liquid and gas phases are no longer differentiable. Triple point: P and T at which solid, liquid, and gas phases can coexist. Molality: moles of solute per kg of solvent. Section III. Basic Problems (3 problems, 10 points each) Be able to find efficiencies and COPs for arbitrary cycles. Simple engines and refrigerators: If I give you a cycle, find everything you can. You will not need to know how to use steam tables for heat engines nor tables for real refrigerators. There will be no questions on liquefaction of gases nor on laser cooling. Be able to tell what quantities are extensive and what quantities are intensive. Know what happens when you combine extensive and intensive quantities in expressions. Be able to work battery and fuel cell problems using Gibbs free enrgy, entropy, and work. Find the theoretical voltage of the battery or fuel cell. Be able to describe and/or draw Fig Be able to describe and/or draw Fig (or the online Maple worksheet) and Be able to describe and/or draw Fig and Understand the van der Waals equation. Describe the Maxwell construction of a van der Waals fluid and how the phase change naturally arises out of the equation of state. Be able to use the ideal gas and dilute solution equations for chemical potential to obtain equilibrium conditions for a chemical reaction. Section IV. Synthesis Problems (2 problems, 10 points each)
3 Sample Test Section I. Review Question See the previous tests. Section II. Qualitative Questions 3. Describe in words Helmholtz free energy and Gibbs free energy. 4. Sketch a diagram for a basic refrigerator. Write the equation of energy conservation involving heat and work. Define the COP. 5. Your friend Isaac decides to invent a new thermodynamic quantity, Isaac s free energy, and define it as I = U + N V S where is a constant which gives correct units. Comment on how useful you think this quantity would be. Section III. Basic Problems 6. A heat engine using N atoms of an ideal monatomic gas is described by the accompanying diagram. Calculate the efficiency of the engine. Also calculate the efficiency of a Carnot engine operating between the same maximum and minimum temperatures. 7. Using the identities on the first page of the test, find what thermodynamic variable is represented by X in the following equation:. Take N for the system to be a constant.
4 8. In a lead-acid battery, the following reaction occurs: The process actually takes place in several steps. The table in the back of the book lists the following at 298 K, one atmosphere, and one molality solutions: Substance S ( J / K ) Pb (s) PbO 2 (s) H (aq) (aq) PbSO 4 (s) HO 2 (l) (a) Find the electrical work per mole of lead produced in a lead-acid cell at the conditions described in the table. The electrical work is the change in the Gibbs free energy. Some energy comes from the environment in the form of heat, but there is no P V work kj (b) Find the heat energy per mole of lead that enters the system. H is kj, this doesn t include the energy from the heat, so the difference is the heat energy going in = kj. ( c) Find the change in internal energy in the system. U H as the volume change is insignificant. (d) Find an expression for the voltage of the cell.
5 Section IV. Synthesis Problems 9. Two substances, A and B, can form three different phases,,, and. A free energy graph at a high temperature is given below. As the temperature lowers, the liquid curve increases free energy more rapidly than the solids. (Assume that all the curves maintain their original shapes and that the solid curves remain essentially fixed with respect to each other.) Draw a phase diagram for the system. Label the eutectics...
6 10. Quartz interacts with water according to the formula: Calculate the molality of quartz that is dissolved in water at 298 K. List numerical values for each of the quantities you would need to include to get the answer. (You do not have to list numerical values of constants, such as k and R.) You may use the following table with data taken from the text. All values are at 298 K. Substance Hint: Assume a dilute solution. The chemical potentials for water and quartz need no correction terms, eg., let.
7 Sample Test Selected Answers Section III. Basic Problems 1. A heat engine using N atoms of an ideal monatomic gas is described by the accompanying diagram. Calculate the efficiency of the engine. Also calculate the efficiency of a Carnot engine operating between the same maximum and minimum temperatures.
8 Section IV. Synthesis Problems 9. Two substances, A and B, can form three different phases,,, and. A free energy graph at a high temperature is given below. As the temperature lowers, the liquid curve increases free energy more rapidly than the solids. (Assume that all the curves maintain their original shapes and that the solid curves remain essentially fixed with respect to each other.) Draw a phase diagram for the system. Label the eutectics...
9 10. Quartz interacts with water according to the formula: Calculate the molality of quartz that is dissolved in water at 298 K. List numerical values for each of the quantities you would need to include to get the answer. (You do not have to list numerical values of constants, such as k and R.) You may use the following table with data taken from the text. All values are for 298 K. Substance Hint: Assume a dilute solution. The chemical potentials for water and quartz need no correction terms, eg., let.
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