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At the top of mountain, a thermometer re...

At the top of mountain, a thermometer reads 280 K and a barometer reads 70 cm Hg. At the bottom of mountain, they read 300 K and 76 cm of Hg. Find the ratio of densities of air at the top and that at the bottom

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By gas equation `PV = (M)/(M_(w)) RT implies (P)/(rhoT) = (R)/(M_(w)) [because mu = (M)/(M_(w))` and ` (M)/(V) = rho]`
Now as `M_(w)` and `R` are same for top and bottom `[(P)/(rhoT)]_(T) = [(P)/(rhoT)]_(B)` So `(rhoT)/(rhoB) = (P_(T))/(P_(B))xx(T_(B))/(T_(T)) = 70/76xx300/280= 75/76 = 0.9868`
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