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Try to derive the barometrical formula for an atmosphere in which the temperature decreases linearly with the altitude. |
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Answer» `T = T_(0) (1 - alpha h)` we obtain `dT = -alpha T_0 dh`. Hence `(dp)/(p) = (Mg)/(alpha RT_0) . (dT)/(T)` Integrating , we obtain In `p = (Mg)/(alpha RT_0) ln T` + const. Since the equation is valid at any point of the gravitaional field, we have on the planet.s surface `ln p_0 = (Mg)/(alpha RT_0) ln T_0 + "const"` SUBTRACTING this force the preceding equation, we eliminate the integration constant to obtain `ln p - ln p_0 = (Mg)/(alpha RT_0) (ln T - ln T_0)` Whence the formula sought for the barometric destribution. |
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