# We showed in class that, for any fluid at rest, the...

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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 = ρ g , where with the z-direction being vertically upward, the gravitational acceleration is g = ge z , and g is a constant (9.8m/s 2 on 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 = ρ R * T , where ρ is 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 p 0 . Solution