Question

At a festival, spherical balloons with a radius of 320. 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 (C2Hg 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 Density of air at 100 °C: 0.946 Density of propane at 100 °C: 1.440 kg kJ Formation enthalpy of propane at 25 °C: 1 - 103.85 — mol

Answer 1

For 1 balloon:

Radius, R = 320 cm = 3.2 m

Volume, V = (4/3 pi R³) = 137.258 m³

Mass of air, m = (volume x density)

= (137.258 m³) x (0.946 kg/m³)

= 129.8 kg

Heat required to inflate 1 balloon:

H = mcAT = (129.8 kg) x (10099/kg°C) x (100°C -25°C)

.H= 9826121.057)

No.of moles of propane available = (given mass) / (molar mass of propane)

= (3000 g) / (44.1 g/mol)

= 68 mol

Heat of combustion of propane, ΔH = 2220 kJ/mol

Hence, Total energy we have, H_total = (2220 kJ/mol) x (68 mol)

= 151020.41 kJ

Therefore, No.of balloons that can be inflated:

N = Hrotal - 151020.41 x 103) 9826121.057)

N = 15.36 15 balloons

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