Chapter 13 examined the variation of pressure with altitude in the Earth’s atmosphere, assuming constant temperature—a model known as the isothermal atmosphere. A better approximation is to treat the pressure variations with altitude as adiabatic. Assume that air can be treated as a diatomic ideal gas with effective molar mass Mair = 28.97 g/mol.
a) Find the air pressure and temperature of the atmosphere as functions of altitude. Let the pressure at sea level be p0 = 101.0 kPa and the temperature at sea level be 20.0 °C.
b) Determine the altitude at which the air pressure and density are half their sea-level values. What is the temperature at this altitude, in this model?
c) Compare these results with the isothermal model of Chapter 13.
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