We have obtained the barometric distribution for the case of an isothermal atmosphere, indeed, in xi 26.10 we assumed the temperature to be the same at every point. Actually, in the real atmosphere the temperature drops with altitude. It may be demonstrated that if the decrease in the temperature with the altitude is linear, i.e. if T = T = T_0(1- alpha h), the barometrical formula assumes the form p/(p_0) = ((T)/(T_0))^(mg//ahT_0) Prove that if a is small this formula reduces to the formula for the barometric distribution in an isothermal atmosphere.

We have obtained the barometric distribution for the case of an isothe

1.	We have obtained the barometric distribution for the case of an isothermal atmosphere, indeed, in xi 26.10 we assumed the temperature to be the same at every point. Actually, in the real atmosphere the temperature drops with altitude. It may be demonstrated that if the decrease in the temperature with the altitude is linear, i.e. if T = T = T_0(1- alpha h), the barometrical formula assumes the form p/(p_0) = ((T)/(T_0))^(mg//ahT_0) Prove that if a is small this formula reduces to the formula for the barometric distribution in an isothermal atmosphere.
Answer» Solution :`p/(p_0) = (1 - ALPHA h)^((MG)/(alpha kT_0)) = [(1 - alpha h)^(-1/(alpha h))]^(-(mgh)/(kT_0)) to E^(-(mgh)/(hT_0))` .

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