A polytrophic atmosphere is defined by the Power-law p/po = (/o) m, where m is an exponent of order 1.3 and po and o are

A polytrophic atmosphere is defined by the Power-law p/po = (ρ/ρo) m, where m is an exponent of order 1.3 and po and ρo are sea-level values of pressure and density.
(a) Integrate this expression in the static atmosphere and find a distribution p (z).
(b) Assuming an ideal gas, p = ρRT, show that your result in (a) implies a linear temperature distribution as in Eq. (2.25).
(c) Show that the standard B = 0.0065 K/m is equivalent to m = 1.235.