Problem Set #2
We showed in class that, for any fluid at rest, the pressure p is the solution to the equation
where with the z-direction being vertically upward, the gravitational acceleration is
and g is a constant (9.8m/s
The ideal gas law is usually written
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
is the mass density of the gas.
What is the relation between the usual gas constant R and R*?
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