Thanks! A helium balloon is used to lift a payload of weight 110N. The weight of

Question

Thanks!

A helium balloon is used to lift a payload of weight 110N. The weight of the balloon itself is 50 N and its volume when fully inflated is 32 m3. The air temperature (assumed to be the same at any altitude) is 0 degree C and the air pressure at ground level is P0 = 105 Pa . The pressure at altitude h is given by P(h) = P0 exp (- mairgh/RT), where mair = 30 x 10-3 kg is the molar mass of air. The balloon is inflated with helium gas. with molar mass mHe = 4 x 10-3 kg. so that the net upwards force on the balloon and its payload at launch is 30 N. How many moles of helium gas are contained in the balloon? At what altitude will the balloon be fully inflated? What maximum altitude will the balloon attain?

Explanation / Answer

Ans
1)
According to archimedes principle,
the net buoyant force is equal to weight of fluid displayed

   air * v*g = 190 N                 (F= 160(total weight)  + 30(upward) )

   PMair *vg/RT =190

  v= 190RT/PMg  = 0.141m3

  PV= nRT

   n=PV/RT  = 6.25
2)   for full inflation 

           P=nRT/V =443.56

    443.56 = 105e-mgh/RT

     5.41 = mgh/RT

      h= 404.79m

 

3)  for max altitude,

 Fnet= 0

    PMair * vg/RT = 160 N                (F= 160(total weight)  + 0(upward) )

      P=373.55

    373.55 = 105e-mgh/RT

      5.58 = mgh/RT

      h= 417.62m

 

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