[1] Derive the pressure-depth (P-z) relationship in a fluid that is compressible with a temperature that varies with z in the following manner: T = T0 z, where T0 is the temperature at the reference depth of z0 and is the lapse rate. Start your derivation with the differential equation: dP/dz = g.

[2] The density for compressible gases can be estimated using the ideal gas law where = PMw/RT = P/RT where R is the universal gas constant. What are the values and units of R and R in SI assuming that the gas is air?

[1] Derive the pressure-depth (P-z) relationship in a fluid that is compressible with a temperature that varies with z in the following manner: T = To - az, where To is the temperature at the reference depth of zo and a is the lapse rate. Start your derivation with the differential equation: dP/dz = - pg. [2] The density for compressible gases can be estimated using the ideal gas law where p = PMW/RT = P/R'T where R is the universal gas constant. What are the values and units of R and R'in Sl assuming that the gas is air? =