b) From the ideal gas law, if the temperature doesn't change, the pressure is directly proportio

Step 1: Start with the expression for dP from part a): dP = -ρgdz

Question

b) From the ideal gas law, if the temperature doesn't change, the pressure is directly proportional to the density. Thus if Po and po are the values of pressure and density at sea level, then P/Po = p/po. Use this to integrate the expression for dP from a) to obtain an expression for pressure P as a function of height z. Defining zo = Po/(pog), where zo is called the scale height, your final expression should be P = Po e^(-z/zo). That is, pressure decreases exponentially with height. Show all steps systematically. Use an extra sheet to complete your work. \frac{P}{P_o} = \frac{\rho}{\rho_o} dP = \rho g dz dP = (\frac{P}{P_o} \rho_o) g dz

          b) From the ideal gas law, if the temperature doesn't change, the pressure is directly proportional to the density. Thus if Po and po are the values of pressure and density at sea level, then P/Po = p/po. Use this to integrate the expression for dP from a) to obtain an expression for pressure P as a function of height z. Defining zo = Po/(pog), where zo is called the scale height, your final expression should be P = Po e^(-z/zo). That is, pressure decreases exponentially with height. Show all steps systematically. Use an extra sheet to complete your work.
\frac{P}{P_o} = \frac{\rho}{\rho_o}
dP = \rho g dz
dP = (\frac{P}{P_o} \rho_o) g dz

b) From the ideal gas law, if the temperature doesn't change, the pressure is directly proportional to the density. Thus if Po and po are the values of pressure and density at sea level, then P/Po = p/po. Use this to integrate the expression for dP from a) to obtain an expression for pressure P as a function of height z. Defining zo = Po/(pog), where zo is called the scale height, your final expression should be P = Po e^(-z/zo). That is, pressure decreases exponentially with height. Show all steps systematically. Use an extra sheet to complete your work.
(P)/(Po) = (ρ)/()
dP = ρg dz
dP = ((P)/(Po) ) g dz

Added by James M.

Question

Please give Ace some feedback