# physics

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A portable steel tank with a volume 35 liters (0.035m³) holds helium gas used for filling party balloons. The pressure in the tank is 120atm when at room temperature of 22 °C. How many moles of helium gas are in the tank?
Each balloon has a volume of 2.5liters when filled with room temperature helium at a pressure of 1.2atm. How many balloons will the tank inflate?
Helium gas particles are single atoms with a mass of four atomic mass units. What is the r.m.s speed of the helium atoms at room temperature 22 °C?

• physics -

The tank has 100 times the pressure of the balloons, and 35/2.5 = 1.40 times the volume

Since the number of moles in proportional to P*V, the tank can fill 1400 balloons.

For the number of moles in the tank, use
n = PV/RT

The RMS speed of the He atoms is
Vrms = sqrt(3RT/M)
where R is the molar gas constant, 8.314 J/moleK
The molar mass for He is
M = 4.0*10^-3 kg.mol

• physics -

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