The balloon, the shell of which has a mass of M = 120 kg, is filled with hot air at a temperature of T = 600 K.

| February 23, 2021 | education

The balloon, the shell of which has a mass of M = 120 kg, is filled with hot air at a temperature of T = 600 K. The ambient temperature is t = 20 degrees Celsius. How much volume must the ball have for it to start rising? The shell of the ball is inextensible. The air pressure inside the ball and atmospheric pressure are the same 10 ^ 5 Pa (M air = 29 ^ -3 kg / mol).

Data: M (mass of the shell of the considered balloon) = 120 kg; T (hot air temperature) = 600 K; t (ambient temperature) = 20 ºС (293 К); P (air pressure) = 10 ^ 5 Pa.

Constants: R (universal gas constant) = 8.314 J / (K * mol); according to the condition Мв (molar mass of air) = 29 * 10 ^ -3 kg / mol.

The volume of the considered balloon is calculated from the inequality: Fa ≥ Fto + Ftv.

ρ1 * g * V ≥ M * g + m * g.

ρ1 * V ≥ M + ρ2 * V.

ρ1 * V – ρ2 * V ≥ M.

V ≥ M / (ρ1 – ρ2).

V ≥ M / (P * Mw / (R * t) – P * Mw / (R * T)).

Calculation: V ≥ 120 / (10 ^ 5 * 29 * 10 ^ -3 / (8.31 * 293) – 10 ^ 5 * 29 * 10 ^ 3 / (8.31 * 600)).

V ≥ 120 / (10 ^ 5 * 29 * 10 ^ -3 / (8.31 * 293) – 10 ^ 5 * 29 * 10 ^ 3 / (8.31 * 600)).

V ≥ 196.9 m3.

Answer: To start lifting, the volume of the balloon in question must be at least 196.9 m3.



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