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The problem states: A paper ball is made which has area of $V=0.1 m^3$ and filled with hot air of temperature $T=340K$. Outside temperature is $T=290K$ while pressure inside the ball and outside the ball is both $p=100kPa$. What should the mass of paper of the ball should be that it would be able to arise in the air?

Note: I've tried using $\frac{p1V1}{T1}=\frac{p2V2}{T2}$ but the answer I get is wrong and I don't actually understand how am I supposed to get volume of surrounding air. Probably that is the case why I can't solve this. Could somebody explain how and why this works?

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  • $\begingroup$ You need to think about the upthrust on the paper ball and the difference in mass of the hot air inside the ball and the mass of the cold air displaced by the ball. In essence you are being asked about the principle behind a hot air balloon. $\endgroup$ – Farcher Feb 22 '17 at 16:47
  • $\begingroup$ You need additional information; the "molecular weight" of air... $\endgroup$ – DJohnM Feb 22 '17 at 20:47
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You don't need the volume of the surrounding air. You need the buoyant force exerted on the ball volume. Check out Archimedes's principle. In your case, the fluid is the surrounding air, and the object being buoyed is the paper forming the ball AND the warmer air inside.

Using the ideal gas law $\left(pV=nRT\right)$, you should be able to calculate the mass of the warm air in the ball, and what would be the mass of cooler air in that same volume. The mass of paper needs to be less than their difference.

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