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PS7.09_short - h increases In this limit what is the...

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2009 Chemistry 118 Problem set #7 Due Friday, November 6 Chapter 13: 32, 36, 44 Chapter 14: 2, 6, 8, 10, 30 Challenge problem #2 Anybody in for another round after the coffee cup challenge? a) In considering Torricelli’s observation of atmospheric pressure, we noted that the weight of the air on the earth was balancing the weight of the mercury pulling down on the surface of the liquid in the inverted tube. But we know that the atmosphere gets thinner as one moves away from the surface of the earth, becoming vacuum in low earth orbit. One way to start thinking about this is to imagine that the temperature of the atmosphere is constant (say at 300 K). Then we might calculate the altitude dependence of the atmospheric density using the perfect gas law. The trick is to balance, at each height, h , above sea level, the downward gravitational pull on a thin slice of the atmosphere with the pressure differential arising from the fact that the air is thinning out as
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Unformatted text preview: h increases. In this limit, what is the pressure 6 miles up, where commercial airliners operate, or 150 miles up, in the neighborhood of the space shuttle?(Ans . The density dies off exponentially ). b) Now we know we were not right in part a), because the pilot is always telling us that the temperature outside our pressurized cabin is some very low temperature, as evidenced by the fact that ice often forms on the windows. This might seem a bit strange at first, because the upper atmosphere is closer to the sun. But if the warming comes from heating the Earth surface, then we might make up a theory where the cooling comes from the heat loss required to pay the work required to raise a volume of gas against the gravitational force. What is the predicted temperature dependence of the atmosphere as a function of altitude in this model, assuming that the atmosphere is so thin that we can take the gravitational acceleration as a constant?...
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