Problem 3:Consider a stationary horizontal slab of air of height dz. Since the slab is at rest, thepressure p holding it up from below must be balanced by the pressure from above PLUSthe weight of the slab.a) Derive a formula for dP/dz the variation of pressure with altitude, in terms of themass density p (greek letter rho) of the air.b) Using the ideal gas law, rewrite the air density in terms of the average mass m ofthe air molecules and other variables. Combine your result with part (a) to derive adifferential equation relating dP/dz to P. Show then that pressure obeys thedifferential equation:dPтgdzkTc) Assume constant temperature T and solve the differential equation in part (b) forpressure P as a function of height z. Assume that P(z=0) is given. Show that thepressure obeys:P = P(0)e-mgz /kTShow also that the density obeys a similar equation.

(a) Write the expression for balanced force equation

Answered: Problem 3: Consider a stationary…

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