Question

A weather balloon is designed to expand to a maximum radius of 22 m at its working altitude, where the air pressure is 0.030 atm and the temperature is 200 K. If the balloon is filled at atmospheric pressure and 258 K, what is its radius at liftoff?

________m

Answer 1

Using Ideal gas law:

PV = nRT

Since number of moles inside balloon and R (gas constant) are constant, Sp

PV/T = Constant

P1V1/T1 = P2V2/T2

V1/V2 = (P2/P1)*(T1/T2)

Using given values:

T1 = 258 K

T2 = 200 K

P1 = 1.0 atm (Since balloon is filled at atmospheric pressure)

P2 = 0.030 atm

So,

V1/V2 = (0.030/1)*(258/200) = 0.0387

Now Volume of balloon is given by:

V = 4*pi*r^3/3

where r = radius of balloon, So

V1/V2 = (r1/r2)^3

r2 = 22 m = max radius

r1 = radius at liftoff = ?

r1 = (V1/V2)^(1/3)*r2

Using known values:

r1 = (0.0387)^(1/3)*22

r1 = 7.44 m = radius at liftoff

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