# ProblemSet2_soln_19.pdf - ECH 141 Problem Set#2 1 We showed...

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ECH 141 Problem Set #2 1. We showed in class that, for any fluid at rest, the pressure p is the solution to the equation p=ρg, where with the z-direction being vertically upward, the gravitational acceleration is g=gez, and g is a constant (9.8m/s2on Earth). a) The ideal gas law is usually written pV=nRT, where T is temperature, p is pressure, V is total volume, n is the total number of moles of gas molecules, and R is the gas constant. In some fluid mechanics texts, the ideal gas law appears as p=ρR*T, where ρis the mass density of the gas. What is the relation between the usual gas constant R and R*? b) Derive an expression for how the air pressure varies with height above the surface of the earth, assuming the temperature T is constant, the elevation is such that gravity is constant, and air behaves as an ideal gas. The pressure at the Earth’s surface is p0. Solution