Question

An approx. spherical balloon with a diameter of 15 m is inflated with He at 20°C.

a. What is the mass of He in the balloon, assuming the gas to be ideal

b. How much work is done by the balloon during the process of inflation against an external pressure of 1 atm, from an initial volume of zero to the final volume?

Answer 1

a) volume of balloon = ( 4/3) x 3.14 x r^2     where r = radius = 15m /2 = 7.5

volum = ( 4/3) (3.14) ( 7.5)^3 = 1767.9 m3 = 1767.9 x 1000 L = 1.77 x 10^6 L

we use PV = nRT to find moles of gas n , where T = 20C = 20+ 273 = 293 K

1atm x 1.77 x 10^6 L = n x 0.08206 liter atm/molK x 293K

n = 73527 mol

mass of He = moles x molar mass of He

     = 73527 mol x 4 g/mol

= 294109 g = 294 kg

b) work done = - P x dV = -P ( V2-V1) = - 1atm x ( 1.77 x 10^6 - 0) = - 1.77 x 10^6 atmliter

we have 1atmliter = 101.325 J

Hence work done = - ( 1.77 x 10^6 atmliter) ( 101.325 J/atmliter)

    = 1.8 x 10^8 J