A hot air balloon works because the ciensity or not air is less than the surrounding cold air.

$($a$)$ The volume of a hot air balloon is $2500m^3$ and its mass is $250kg($without passengers$).$ The temperature of the air in the balloong

Density of air at $20C=1\mathrm{.}21kg{m}^{-3}$

Awerage relative molecular mass of air $=29gmo{l}^{-1}$

$($i$)$ Calculate the volume of $1kg$ of at $20C.$

$($ii$)$ Calculate the volume of $1kg$ of air at $100C$ and hence show they the density of air at $100C$ is $0\mathrm{.}95kg{m}^{-3}.$

$($iii$)$ Calculate the mass of hot air in the balloon.

$($iv$)$ Calculate the mass of cold air displaced by the balloon.

$($v$)$ Determine whether the balloon will leave the ground or not.

b$)($i$)$ Calculate the average velocity of air molecules in the balloon $($assume the molecules behave as spheres$).$

$($ii$)$ Calculate the number of moles in the balloon.

$($iii$)$ Calculate the internal energy contained by the hot gas