5. (4 pts) conservation of energy and some (thermo)dynamics: expression for the density p that results when an air parcel initially at pressure a) derive an ps and density ps expands adiabatically to pressure p. only use these four variables and associated constants. b) using the above, lifted dry adiabatically. what is its density when it reaches the 500 hpa level? an air parcel that has a temperature of 20°c at the 1000 hpa level is