Aballoon is filled with helium at a pressure of 2.4 x 105 pa. the balloon is at a
temperature of 18 oc and has a radius of 0.25 m. (a) how many helium atoms are
contained in the balloon? (b) suppose we double the number of helium atoms in the
balloons, keeping the pressure and the temperature fixed. by what factor does the radius
of the balloon increase?

1)
p = 2.4 * 10^5 Pa
T = 18° C + 273.15 = 291.15 k
r = 0.25 m => V = [4/3]π(r^3) = [4/3]π(0.25m)^3 = 0.06545 m^3 = 65.45 L

Use ideal gas equation: pV = nRT => n = pV / RT = [2.4*10^5 Pa * 0.06545 m^3] / [8.31 J/k*mol * 291.15k] = 6.492 mol

Avogadro number = 1 mol = 6.022 * 10^23 atoms

Number of atoms = 6.492 mol * 6.022 *10^23 atom/mol = 39.097 * 10^23 atoms = 3.91 * 10^24 atoms

2) Double atoms => double volume

V2 / V1 = r2 ^3 / r1/3

2 = r2 ^3 / r1 ^3 => r2 ^3 = 2* r1 ^3

r2 = [∛2]r1

The factor is ∛2

Jet streams are relatively narrow bands of strong wind in the upper levels of the atmosphere. the winds blow from west to east in jet streams but the flow often shifts to the north and south. jet streams follow the boundaries between hot and cold air. the earth's rotation is responsible for the jet stream as well.