A Balloon is to be filled from a helium tank. The tank is large and the tank pre

Question

A Balloon is to be filled from a helium tank. The tank is large and the tank pressure remains effectively constant while the balloon is filled. A valve between the tank and the balloon controls the helium flow to a constant rate of 0.05kg/s. The pressure in the balloon varies during the filling process. The temperature of the helium entering the balloon is 20'C

1) How much work is done in filling the balloon to a final pressure of 500kPa, where the final radius is 2m if the balloon is adiabatic (it takes 8min to fill the balloon)

2) What is the final Temperature in the balloon?

Explanation / Answer

a) first start with conservation relations.

m2 - m1 = min

where m1 = 0 (assumed empty at beginning)

E = (mu)2-(mu)1 = hinmin - W12,out

For ideal, monatomic gas (helium),

Cp = 5/2 R = 5.193 kJ/kgK

Cv = Cp - R = 3.116 kJ/kgK

R = R'/m = 2.077 kJ/kgK

After 8 minutes, mass is

m = 8 * 0.05 * 60 = 24kg

Now,

W12,out = CpTinmin - Cv/R * (PV)2

using the above calculated values, plug in. Where P = final pressure = 500kPa and V is the volume of a sphere = 4/3 r3.

W12,out = (5.193)(293)(24) - (3.116/2.077)*(500 * 4/3 * * 23)

W12,out = 11,380 kJ

b)

Ideal gas law: PV = mRT

T = PV/mR

Where PV = (500 * 4/3 * * 23)

mR = (24 * 2.077)

Thus,

T = (500 * 4/3 * * 23)/(24 * 2.077)

T = 336K

Please don't forget to rate, I hope this helped! :)

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