Question

At a festival, spherical balloons with a radius of 160. 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. 1.00 kg of butane (C,Hfuel 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 g.C kg 0.946 3 m Density of air at 100 °C: kg 1.898 3 m Density of butane at 100 °C: kJ -125.7 mol Formation enthalpy of butane at 25 °C Any other data you need should be taken from the ALEKS Data resource. balloons ?

Answer 1

The heat released by the burning of butane is calculated according to the equation:

C4H10 + 13/2 O2 = 4 CO2 + 5 H2O

ΔH = (4 * -393.5) + (5 * -241.8) - (-125.7) - (13/2 * 0) = - 2657.3 kJ / mol

q butane = 1000 g * (1 mol / 58.12 g) * (2657.3 kJ / 1 mol) = 45720 kJ

The mass of air required to fill a balloon is calculated:

m air = 4 * π * r3 * d / 3 = 4 * π * (160 cm) ^ 3 * 9.46x10 ^ -4 g / mL / 3 = 16230 g

The heat that is required to fill a hot air balloon is calculated:

q balloon = m * cp * ΔT = 16230 * 1,009 * (100-25) / 1000 = 1228 kJ

The number of balloons is calculated:

balloons = q butane / q balloon = 45720/1228 = 37.23 balloons

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