A planet's atmosphere contains a perfect gas with polytropic equa-tion, p = Ap, where p is the pressure, p is the density, y is thepolytropic index and A is a constant. Assuming that the accelerationdue to gravity, g, is practically constant with height:a) i) show that the expression of the ratio of the pressure, p (at avertical height z from the surface in terms of the surface pressure), toPo (the surface height), and the surface temperature To is:²₁ = (₁ - (^² = ²¹);(2)Р1Powhere y is the adiabatic constant and the gas constant is R.gRT.-Zii) Use the equation in 1) a) i) to find the numerical value of thetemperature lapse dT/dz, given that g = 9.8 m/s², R = 287 Nm/kgK, and y 1.23.=

The objective of the question is to derive the expression for the ratio of the pressure at a height…

Answered: A planet's atmosphere contains a…

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