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# HW 2 - Professor Philip S Marcus ME106 Homework Problem Set...

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09/09/09 Professor Philip S. Marcus ME106 Homework Problem Set 2 - Pressure Do Problems in Chapter 2 (6 th edition): 2.29, 2.34, 2.58 and 2.61. (or equivalently, in the 3 rd edition: 2.25, 2.34, 2.52, and 2.64). O2.1) Find expressions for the density ρ ( z ) and entropy S ( z ) of an isothermal at- mosphere as a function of height z and the density ρ 0 and entropy S 0 at sea level (assumed to be at z = 0.) Now make a plot (use MATLAB or any other program- ming tool you want) of the density as a function of height assuming that the pressure at sea level is 14.7 pounds per square inch and that the temperature is 310 K. Start, by using P = ρ R T and the value of R for air from Lecture 1 by finding the value of ρ 0 . What is the functional form of the entropy as a function of height (i.e., ex- ponential, logarithmic, power-law, linear, cubic, quadratic, etc.)? In an isothermal atmosphere does the entropy increase or decrease with increasing height? O2.2) If the density of the atmosphere were in hydrostatic equilibrium and ρ ( z ) = ρ 0 - α z , what are T ( z ), P ( z ), and S ( z ) in terms of α , ρ 0 , g , P 0

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HW 2 - Professor Philip S Marcus ME106 Homework Problem Set...

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