EK424 HW2+solutions - Fall 2018 PDF

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Fall 2018...

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EK424 HOMEWORK 2 (due Thursday, September 20, 2018) Problems 1-4 are on your own; you may solve problem 5 in groups. 1. Critique the following statement: “The heat added to an object is the product of its heat capacity and the change in temperature, both of which are path-independent. Therefore, the heat added is also pathindependent.” 2. You have one liter of ideal air at 300 K and 1 atm. You add 10 J of heat to it while holding pressure constant. What is the final volume? 3. One liter of ideal air undergoes the “N”-shaped path on the P-V diagram. Starting from 1 atm and 300 K, the air is pressurized isochorically to 3 atm. Then it expands adiabatically, until the pressure drops back to 1 atm. Then it is pressurized isochorically once more to 3 atm. Find ΔU, Q, and W for the whole process. 4. Let’s consider the complete vaporization of 1 L of water at a pressure of 1 atm. The conversion of water into H2O vapor takes place at 100°C. During this process, neither the pressure nor the temperature change. A) What volume of vapor is created? The density of water is 1 g/mL. Assume that the vapor is an ideal gas. B) How much work is performed by the H2O? C) The amount of heat needed to boil water is 41 kJ/mol. What is the change in internal energy of the H2O? D) What is the heat capacity CP for water vaporization? 5. In reality, air is not totally composed of diatomic gases. Instead, it is 99% diatomic (N2 and O2) and 1% monatomic (Ar). That is, 1 mol of air contains 0.01 mol of argon. Assume air is ideal. A) The internal energy of air is proportional to temperature, with U = βnRT, where n is the number of moles of air. In class, we found that β = 5/2 for purely diatomic gases. Find β for air, taking into account the trace amount of Ar. B) During an adiabatic change of air, PVγ is a constant. In class, we found that γ = 7/5 for purely diatomic gases. Find γ for air, taking into account the trace amount of Ar. C) Based on your answers in (A) and (B), justify the treatment of air as a purely diatomic gas when calculating ΔU, Q, and W. In other words, if you use β = 5/2 and γ = 7/5, is the error in the calculated energy roughly 10%, 1%, 0.1%, 0.01%, or even smaller? No need to be super exact, only order-of-magnitude estimates are needed....