Question

Air at temperature of 400 K and atmospheric pressure is filled in a balloon of volume $1m^3$. If surrounding air is at temperature of 300 K, if the ratio of Buoyant force on balloon and weight of air inside is $x/3$, find $x$.

Answer 1

$Buoyantforce=V\times density\left(out\right)\times g$
$weight=V\times density\left(in\right)\times g$
Hence, $\frac{\text{Buoyant force}}{wight}=\frac{density\left(out\right)}{density\left(in\right)}=\frac{temp\left(out\right)}{temp\left(in\right)}=\frac{400}{300}=\frac{4}{3}$
Note : The ideal gas equation is $PM=DRT$
Hence, when P and M are constant, the density is inversely proportional to the temperature.