A spherical balloon is made from a material whose mass is 3.05 kg. The thickness

Question

A spherical balloon is made from a material whose mass is 3.05 kg. The thickness of the material is negligible compared to the 2.06-m radius of the balloon. The balloon is filled with helium (He) at a temperature of 284 K and just floats in air, neither rising nor falling. The density of the surrounding air is 1.19 kg/m3. Find the absolute pressure of the helium gas. Because the balloon is in equilibrium, the buoyant force acting on the balloon equals its weight, where its weight is equal to the weight of the balloon plus the weight of the helium inside the balloon. Use this relationship to find the weight (thus the mass) of the helium. (Review section 11.6.) With the mass of the helium known, the number of moles of helium can be calculated (see section 14.1). With the number of moles known, the ideal gas law can be used to calculate the pressure of the helium gas.

Explanation / Answer

Let be the density of helium inside the balloon. The net force is zero so mg=V*g*(1,19-) so =-m/V +1,19=1,19-3,05/(4/3r^3)=1,11(kg/m3). Let P be the pressure of helium PV=nRT n*/V=P/RT= so P=RT/=6,53e5(Pa)

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