Chapter 18, Problem 76P

The adiabatic lapse rate is the rate at which air cools as it rises and expands adiabatically in the atmosphere (see Application: Smog Alert, on page 324). Express dT in terms of dp for an adiabatic process, and use the hydrostatic equation (Equation 15.2) to express dp in terms of dy. Then, calculate the lapse rate dT/dy. Take air’s average molecular weight to be 29 u and γ = 1.4, and remember that the altitude y is the negative of the depth h in Equation 15.2.