# A hot air balloon is a sphere of radius 8 m. The sir inside is at a temperature of . How large a mass can the balloon lift when the outside temperature is ?

The amount of pressure outside a balloon is lesser than the amount of pressure inside the balloon.

{: surface tension, R: balloon’s radius}

Where, V is the volume of balloon and ni is number of moles of gas in the balloon

R is the gas constant, Ti is the temperature

= Mass of balloon (Mi)/Molecular mass (Ma)

-------------(1)

In the same way,

According to principal of floatation, , here W is the weight which the balloon lifts

If the mass displaced by balloon is M0 and Ma is the mass inside or outside of the balloon

---------------(2)

Hence from (1) and (2) we can write,

Ma = 79% N2 + 21%O2

+ Pressure due to ST of membrane

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