About question of prove in thermodynamics

[opeth_35]

I have started new to learn thermodynamics but i can't continue about this two problems. If you help me . I will appreciate about that.. actually How should I continue? what is going to be my approach? I wonder this.
thank you.

Problem 1.16. The exponential atmosphere.
(a)
Consider a horizontal slab of air whose thickness (height) is dz. Ifthis slab is at rest, the pressure holding it up from below must balance both the pressure from above and the weight of the slab. Use this fact to find an expression for dP/ dz, the variation of pressure with altitude, in terms of the density of air.
(b)
Use the ideal gas law to write the density of air in terms of pressure, temperature, and the average mass m of the air molecules. (The information needed to calculate m is given in Problem 1.14.) Show, then, that the pressure obeys the differential equation

Problem 1.14. Calculate the mass of a mole of dry air, which is a mixture of N2 (78% by volume), 02 (21%), and argon (1%).

 

[NateD]

(The atomic masses are 14.0 for N2, 32.0 for 02, and 39.9 for argon.)Answer: Problem 1.16: (a) Consider a horizontal slab of air whose thickness (height) is dz. If this slab is at rest, the pressure holding it up from below must balance both the pressure from above and the weight of the slab. Thus, the total pressure, P, is given by the equation: P = P + mgdz where m is the mass of the air in the slab, g is the acceleration due to gravity, and dz is the thickness of the slab. Taking the derivative with respect to z, we obtain: dP/dz = mg Thus, the pressure varies linearly with altitude, if the mass of air in the slab is constant. (b) Using the ideal gas law, the density of air can be written as: ρ = P/RT where P is the pressure, T is the temperature, and R is the universal gas constant. To calculate the mass of a mole of dry air, we can use the information given in Problem 1.14. The mass of a mole of dry air is: m = (14.0*0.78 + 32.0*0.21 + 39.9*0.01) / 6.02 x 10^23 Substituting this expression into the ideal gas law equation, we obtain: dP/dz = (mRT)/g Therefore, the pressure obeys the differential equation: dP/dz = (mRT)/g