When working out the numerical problems, make sure you use a consistent set of units.

1. Cabin pressure in a typical commercial airliner is equivalent to a height of 1.7 km above sea level. If the sea level pressure and density of air are 1000 mbars and 1.25 kg/m^-3 respectively, what is the air pressure and density at this altitude?
   
   
2. The mass flux of air into the topical belt located between +/- 15 degrees is 1.3 x10¹¹ kg/s. If this air contains 20 g of water vapor per kg of air, what would be the daily annual rainfall rate assuming that all of the water vapor does fall out as rain. Hint: treat the surface from -15 to +15 as a cylinder.
   
   
   Note: unit conversions for this problem are a bit tricky so make sure you do a reality check on your final numerical answer.
   
   
   
3. Consider two water parcels each at a pressure of 1 bar. Parcel A has a salinty of 34 ppt and a temperature of 32 C. Parcel B has salinty of 25 ppt and temperature of 0 C. Both have equal densitys of 1020 kg/m³. Assume that both parcels have equal speeds of sound at 1500 m/s.
   
   
   
   

   a) Show that if equal parcels of water are mixed, the mixture would be more dense than the original densities (this is strongly related to salinty driven currents in the real ocean)

   b) If both water parcels are adiabatically compressed to a pressure of 100 bars (remember they start at 1 bar), what are their respective densities ( hint: adiabatic compression is related to the speed of sound, which is the same for both parcels)

   c) At 100 bars, show that Parcel A will still be warmer than Parcel B
   
   4. A dry air parcel of volume = 1 km³ ascends from 1000 mb to 700mb. Assuming that it does not mix or exchange heat with its environment and that it has an initial temperature of 10 C. Calculate the following (in SI units):
   
   

   • The initial density of the parcel
   • The final temperature and final density of the parcel
   • The change in internal energy of the parcel
   • The overall work done by the parcel during its ascent

5.