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1. Enthalpies of reaction and heating a) You need to haul your fuel and store it so that the quantity of most interest to you is the number of kJ you get for combusting a fixed weight of it. Determine whether gasoline (octane), liquefied natural gas (CH4(1)) or biofuel (ethanol) is your preference giving the number of kJ per kg you can generate. b) You would like to heat the air (assume it is all nitrogen and oxygen at 295 K) in a well insulated room that is 4x 6 X 3 cubic meters in size by 5 degrees Celsius using the heat from a combustion reaction. Assuming you can transfer the heat of reaction perfectly into the air, how much of your fuel will you need? (Note: For the purposes of this problem, you should make the realistic assumption that the pressure is constant at 1 atm. Also, please use a simple estimate for the specific heats of oxygen and nitrogen that neglects vibrational excitation rather than doing complex calculations.) c) Suppose we tried a more sophisticated model of the specific heat accounting for vibrational modes. Would I calculate that I need to use more fuel or less (explain how you know)? d) Suppose that all of the oxygen in the room happened to be composed of the 180 isotope rather than the common isotope? Would that make the computed amount of fuel needed increase, decrease or stay the same? Explain your answer. 2. Engine efficiencies and useful work We defined efficiency of an engine by the ratio of work done in a full cycle on a P-V plot to the heat put in during the expansion. I asserted that the Carnot cycle (isothermal expansion at Th followed by adiabatic expansion followed by isothermal compression at T1 followed by adiabatic compression) produces the most efficient possible engine for a given amount of expansion V min V max. a) You are interested in the following alternative way to expand which is to isothermally at In expand all the way to Vmax and then lower the temperature to T1. while holding the system at constant volume. After that, you do the reverse and isothermally contract all the way to Vmin and raise the temperature while holding the volume constant. Calculate the efficiency for the alternative process and prove that it is lower than the Carnot engine efficiency. b) Explain this result physically - in other words, why did you need to either put in more energy or why did you get out less work? Pressure Solid line = Carnot Solid plus dashed = alternative Vmin Vmax Volume

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