An important factor in determining the extent of air pollution in urban areas is whether the atmosphere is stable (poor mixing, accumulation of pollutants) or unstable (good mixing and dispersion of pollutants). Whether the atmosphere is stable or unstable depends on how the temperature profile (the so-called lapse rate) in the atmosphere near ground level compares with the “adiabatic lapse rate.” The adiabatic lapse rate is the atmospheric temperature that would result at each elevation if a packet of air (for example, as contained in a balloon) rose from ground level without any heat or mass transfer into or out of the packet. Assuming that air is an ideal gas, with a molecular weight of 29 and a constant-pressure heat capacity of 29.2 J/(mol K), obtain expressions for the pressure profile and the adiabatic lapse rate in the atmosphere.