Question

1. For the earth, an estimate of the variation of pressure with altitude above the surface of the earth is made for a gas of molecular weight, M, assuming the atmosphere is isothermal, the variation of g with altitude is negligible, and that the atmosphere behaves like an ideal gas. A significant error in this estimate arises from the assumption that the temperature of the atmosphere, T, is isothermal instead of decreasing with altitude. This decrease with altitude y in the troposphere is given roughly by, where Te is the temperature at the surface of the Earth and B is a constant that is roughly equal to 6 °C/km. (a) Under these assumptions how does the pressure vary with altitude in terms of the altitude, y, molecular weight of the gas, M, gas temperature, T, and appropriate constants? (b) What is the pressure using your result in (a) at the typical altitude an airliner flies, say 35,000 ft? Take TE 293 K and the pressure at the surface of the earth to be 1 atm. (c) How does your answer in (b) compare to the case where you assume an isothermal atmosphere, that is when p 0?

Answer 1

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