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**1. Homework Statement**

A helium meteorological balloon is made of a bag of impervious fabric that does not stretch, and when fully inflated forms a spherical shell of 1m diameter enclosing the He. At launch it is filled with He (at STP) to 15% capacity. The launch takes place in the Antarctic, in winter, at a temperature of 220K, so it is reasonable to assume that the temperature does not vary much with height. Note all assumptions and approximations made.

a)What volume does the balloon occupy at launch at sea level?

b)What mass of He is in the balloon?

c)What is the mass of air displaced by the balloon at sea level?

d)Estimate the buoyancy force at launch.

e)After launch the balloon rises. Estimate the buoyancy force when it has reached an altitude of 2km.

**2. Homework Equations**

PV = nRT

n=m/M

V=4/3[tex]\pi[/tex]r

^{3}

**3. The Attempt at a Solution**

a)V=4/3[tex]\pi[/tex] x 0.5

^{3}x 0.15 = 0.0785m

^{3}

b)No densities were given.

PV = nRT. Therefore n = PV/RT.

P = 1.013x10

^{5}Pa (given from formula sheet)

T = 273K

**<-- Should this be 220K?**

V = 0.0785m

^{3}

M = 4 atomic mass units (given)

Therefore n = 3.504mol

m=nM = 3.504 x 4 =14.01g

c) Mass displaced = mass of Helium = 14.01g.

d)

m = 14.01/1000 = 0.014kg

Buoyancy force = weight of volume displaced = mg = 0.137N

e)From a) and b), density = m/V = 0.014/0.0785 = 0.178kg/m

^{3}

At 2km, P=75100Pa (given). n, R and T remain constant.

V = nRT/P = (3.504 x 8.314 x 220)/75100 = 0.0853m

^{3}

Assuming density remains constant as altitude changes,

m=density/Volume = 0.178/0.0853 = 0.0152kg.

Buoyance force = 0.0152 x 9.8 = 0.149N

Basically, I'm just not sure if this is correct and want someone to check if my working out is all right :) The part I'm most unsure of is part e) and the fact that the buoyancy forces are so small!.