Question

A helium balloon is used to lift a load of 100 N. The weight of the envelope of the balloon is 45.0 N and the volume of the helium when the balloon is fully inflated is 31.8 m³. The temperature of the air is 0°C and the atmospheric pressure is 1.00 atm. The balloon is inflated with a sufficient amount of helium gas that the net upward force on the balloon and its load is 31.2 N. Neglect any effects due to the changes of temperature as the altitude changes.

(a) How many moles of helium gas are contained in the balloon?
mol

(b) At what altitude will the balloon be fully inflated?
km
(c) Does the balloon ever reach the altitude at which it is fully inflated?

Yes/No   

(d) If the answer to Part (c) is "Yes," what is the maximum altitude attained by the balloon? (If the answer to Part (c) is "No", enter no.)
km

Answer 1

3. Solution a) weight of load = W Load = 100 N weight of envelope - We = 45 N volume of balloon when fully inglated = Vo = 31.8 m atmospherie Temperature = To = 0°C -243K atmospheric press wie Po = 1 atm 1•0132 5x 10px a S

Let n be the number of Moles Density of air = Pa = 1.225 kg /m² Density of Helitho = Sue = 0.178 kg/mol Fo = Net upward for ce = 31.2N n = Po(For Wet Wroad) R TolPa - Sue) g. con = 1x ( 31+2 +45 +100) 0.0821 x 273 x ( 10225 -0.178)x98 n = 0.766 more. Solution b) Yo be the height at which the balloon is fully inflated. .. Yo = un ( love ) = ln at 1:0 (325x10x3108) nRTO Yo = = 7.524m = 7.524 x 10 Km. solution c) if nR Tog (Pa - Sug) > Wroad & We the Ballon will reach the Height yo withe fully infloded size 0.766*0:0821x 27389°8 x (1.225-0.178) 1 = 176-16 > 145 in yes the balloon will reach the attitude at which it is fully infated Let 0.706x8314x273 ९०

Solutiond) Maximum Height altitude attained by the balloon with fully inflated size Yo = 7:52.4x 10° Km. -3