[Single-digit Integer] What will be the temperature difference (in °C) needed in a hot air balloon to lift 10.0 / 8.314 kg of mass? Assume that the volume of the balloon is 91.0 m^3, the temperature o

Question

[Single-digit Integer] What will be the temperature difference (in °C) needed in a hot air balloon to lift 10.0 / 8.314 kg of mass? Assume that the volume of the balloon is 91.0 m^3, the temperature of the ambient air is 17°C, the pressure is 1.0 bar, and air is an ideal gas with an average molar mass of 29 g/mole.

Prashant Kotian · Accepted Answer

Correct answer: 4. The lifting force is equal to the difference in mass of the cold ambient air and hot air inside the balloon: Δm = V × P × M / R × (1/T_cold - 1/T_hot) = 10 / 8.314 kg. Given T_cold = 290 K, P = 10^5 Pa, V = 91 m^3, M = 0.029 kg/mol. Solving for T_hot gives T_hot = 294 K. The temperature difference is ΔT = 294 - 290 = 4°C. Thus, the integer answer is 0004.

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