Fluid dynamics of Earth Atmosphere and Climate - Midterm exam - March 2015
Please write your name on each page.
1. Consider an air parcel at T = 300K and ρ = 1kg m-3 .
a. Determine the air pressure using the ideal gas law.
b. If the parcel contains 10 gram of water vapor per kilo of dry air, determine the partial pressure of water vapor.
c. How much water vapor should be added to this air parcel to bring it to saturation, knowing that the saturation vapor pressure at 300K is es = 3500Pa.
(The ideal gas constant for dry air is Rd = 287JK-1kg-1 . The ideal gas constant for water vapor is Rv = 460JK-1kg-1.)
Please clearly write down the formulas you are using for the computation. You need only to carry the computation to the first two digits.
2. Below is a reproduction of the figure 2.7 from the textbook showing the energy fluxes in the simple greenhouse model.
a. Briefly define each terms (namely Ta , Ts , S , A, S0 and α) shown in the figure.
b. What is the physical law that relates the radiation flux A and S to the temperature of the atmosphere and surface?
c. Write the energy budget for the Earth surface, for the atmospheric layer and for the whole planet (surface and atmosphere combined) as described by the figure.
d. Determine the temperature of the surface as function of the incoming solar radiation S0 and the albedo α .
3.a. Explain the concept of buoyancy.
b. Write the expression for the buoyancy of an air parcel as function of its density卩p and that of the environment卩e.
c. By taking advantage of the ideal gas law, express the buoyancy of an air parcel as function of its temperature. (You can assume that the parcel pressure is the same as that of the environment.)
d. What is the acceleration in a hot air ballon filled with warm air at T = 360K while the outside air is at T = 300? If the mass of air in the ballon is 1000kg, how much additional weight can it carry in the basket?
4. For an adiabatic parcel, the first law of thermodynamics can be written as
where Cp = 1000 JK-1kg-1 is the heat capacity of dry air at constant pres- sure, T is the parcel temperature, g = 10ms-2 is the gravitational accelera- tion, and Z is its altitude.
a. From this equation, derive the adiabatic lapse rate.
b. Provide a physical explanation as to why the temperature decreases as an air parcel rises (in other words, explain the concept of the adiabatic lapse rate to one of your friend who has not taken the course.)
c. Inside a cloud, equation (1) does not hold any more. Discuss how conden- sation afects the adiabatic ascent?
d. How would you modify equation (1) to account fro the efect of conden- sation?