Question

A tank with a volume of 0.150 m3 contains 27.0oC helium gas at a pressure of 100 atm. How many balloons can be blown up if each filled balloon is a sphere 30.0 cm in diameter at 27.0oC and absolute pressure of 1.20 atm? Assume all the helium is transferred to the balloons.

Answer 1

884 balloons

Step-by-step explanation:

Assume ideal gas, since temperature is constant, then the product of pressure and volume is constant.

So if pressures reduces from 100 to 1.2, the new volume would be

`V_2 = (P_1V_1)/(P_2) = (100*0.15)/(1.2) = 12.5 m^2`

The spherical volume of each of the balloon of 30cm diameter (15 cm or 0.15 m in radius) is

`V_b = (4)/(3)\pir^3 = (4)/(3)\pi 0.15^3 = 0.014 m^3`

The number of balloons that 12.5 m3 can fill in is

`V_2/V_b = 12.5 / 0.014 = 884`