Question

At a festival, spherical balloons with a radius of 140. cm are to be inflated with hot air and released. The air at the festival will have a temperature of 25 °C and must be heated to 100 °C to make the balloons float. 3.00 kg of propane C H ) fuel are available to be burned to heat the air. Calculate the maximum number of balloons that can be inflated with hot air. Here are some data you may find useful: Specific heat capacity of air: 1.009 0.946 Density of air at 100 °C: Density of propane at 100 °C: Formation enthalpy of propane at 25 °C: -103.85 mol Any other data you need should be taken from the ALEKS Data resource. balloons balloons x 6 ?

Answer 1

Answer :- 8.6 balloons

Explanation :-

Formation of enthalpy of propane = -103.85 kJ/mol

Mass of propane = 3 kg = 3000 g

Molar mass of propane = 44 g/mol

Now,

1 mol propane = -103.85 kJ

ie. 44 g of propane = -103.85 kJ

therefore,

3000 g propane =
3000(9) X-103.85(kJ) P= -7080.68 (kJ) 44(9)

here, negative because, heat is released by burning of propane.

but this heat is absorbed by air

so heat absorbed by air = 7080.68 (kJ) = 7080680 (J)

Since, temperature of air increased from 25 °C to 100 °C

i.e T_i = 25 °C and T_f = 100 °C

Therefore,

Mass of air calculate by using formula

q=mCAT

ie.
q=mC(T: - T;)

C = specific heat capacity of air = 1.009 J/g.°C

therefore,

7080680(I) = m 1.009(J/g. c) (100(°C) – 25(°C))

i.e
7080680(J) 1.009(J/g.'C) x 75(°C) = 93566.96(9)

ie. mass of air =
m = 93566.96(9) = 93.567 kg

Now we know that

volume of sphere = V =  $\frac{4 \pi r^{3}}{3}$

r = 140 cm

Therefore,

4 x 3.143 x (140(cm)) V =

4 x 3.143 x 2744000(cm) V =

V = 11499189.33(cm) = 11.499(m)

This is the volume of air in one balloon at 100 °C

Now, calculate mass of air in one balloon at 100 °C

We have , density of air at 100 °C = 0.946 kg/m³

we know,
Mass = Density x Volume

therefore,

Mass = 0.946(kg/m) x 11.499(m)

Mass = 10.878(kg)

I.e mass of air in one balloon = 10.88 kg.

Number of balloons inflated with hot air are calculated by dividing mass of air by mass of air in one balloon as

Masso f Air NumberOf Ballon = Mass Of Air InOne Ballon
  

93.567 kg Number Of Ballon=; 10.878(kg)

NumberOf Ballon = 8.6

Therefore, 8.6 balloons can be inflated with hot air.