Thermodynamics -- hydrostatics question

[nataliarodri]

Good afternoon. You are a student of the career of physical I am 'm like someone aids with the second section (II) the following problem because I do not understand much.

Thank you very much.
Problem:
Considering that the effects of pressure variation with height are due only factor hydrostatic (dp/dz =(rho)g)), say what is the end of a mass of an ideal gas diatomic when quasiestàticament up the atmosphere from an initial state? (Z1, T1, p1 )up to a certain height Z2. Do the calculation for two different cases:
(i) assuming that the process is adiabatic (check in this case what value it has, itself, the variation of temperature with height);
(ii) in the case where the gas entropy wins in proportion to the height trail, ds = (alpha)dz.

 

[Ken G]

You need to use ds = alpha dz to get P as a function of rho, and then just solve for the differential equation in rho(z). It will help that the ideal gas connection between entropy and P/rho is dq/ds = (P * m) / (rho * k), right? Here dq is the heat added, so dq = du - P*m/rho² drho, and u=5/2 * P * m / (rho * k) for a diatomic gas. Notice that I've avoided using T anywhere, as it plays no explicit role and is just being substituted away. The goal is to get one differential equation that gives you dP/drho as a function of P and rho, and another that gives you dP/dz as a function of rho, and eliminate P. You can always set alpha=0 at the end to get part (i).