Hot air ballooning

You are a maker of hot air balloons and wish to construct a balloon that will lift you and a friend to places unknown. Your standard balloon design is a perfectly spherical, nylon fabric balloon with a small hole on the bottom for the burner that heats the air. Nylon starts to degrade if the air temperature exceeds $120^\circ\mbox{C}$, so you don't want to exceed this temperature for your hot air. What is the minimum radius in meters you need for your balloon?

Details and assumptions

• You, your friend, the balloon, the burner, and the basket have a total mass of $300~\mbox{kg}$.
• The ambient pressure is $1~\mbox{atm}=101,325~\mbox{Pa}$ and the temperature of the surrounding air is $20^\circ\mbox{C}$.
• Air has a molar mass of $\mu=29~\mbox{g/mol}$.
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