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MT1-cheatsheet

# 37 105 j we find the work from cp ql w 609 237 105

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Unformatted text preview: sider an iron meteorite of mass M = 1 kg falling to Earth at night. At a height h = 20 km, the frictional and gravitational forces cancel one another and the meteorite thus reaches terminal velocity vterm = 50 m/s. At this moment, let t = 0 and the temperature of the meteorite be T0 = 300 K. For simplicity, let's assume that the meteorite is perfectly spherical. Possibly useful numbers: density iron = 10 gm/cm3 emissivity iron = 1/3 heat of fusion Liron = 250 kJ/kg melting point Tmelt = 2000 K specific heat ciron = 1/2 J/(gm K) a) What is the rate of heat flow into the sphere due to air friction? Assume that all the heat generated by friction goes into the sphere. Now assume that the sphere is a blackbody. b) What is the rate of heat loss due to radiation when the sphere is at a temperature T? c) How does the temperature change with time? All we need is a differential equation for T(t), you don't need to solve it! d) What is the maximum temperature that the meteorite can get to with our simplified falling assumptions? Will it have melted before it hits the ground? Problem 3 (25 points). Consider some helium gas in box. Temperature T, volume V, pressure P. a) What is the number N of helium atoms in the box? Now open a small hole in the box and let gas escape into another box that is completely empty, and has volume 0.1 V. b) What is the change in internal energy of the helium gas? Explain in 1 sentence. c) The number of microstates is proportional to VN. By what factor have the number of microstates changed? d) What is the change of entropy? Ok so far so good. We just changed the entropy of the gas by letting it expand. But there is another way to change the entropy of the gas: we can heat or cool it. e) Same initial conditions as before. To which final temperature must we (heat/cool) the helium so that its entropy changes by the same amount as in problem d? If you are unsure of your answer for problem d, assume that the entropy change is S. Hint 1: for a monoatomic gas at constant...
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