A balloon carries a total load of 185; text{k | vedclass

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Question

(D) The lift capacity of a balloon is proportional to the density of the displaced air,which is determined by the ideal gas law $PV = nRT$ or $P = \rh

Vedclass · Accepted Answer

$123.54$

Vedclass · Answer

(D) The lift capacity of a balloon is proportional to the density of the displaced air,which is determined by the ideal gas law $PV = nRT$ or $P = ho R T / M$.Since the volume $V$ is constant,the mass of the displaced air $m = ho V$ is proportional to $P/T$.Given: $P_1 = 76\; 	ext{cm of Hg}$,$T_1 = 27 + 273 = 300\; 	ext{K}$,$M_1 = 185\; 	ext{kg}$.At height: $P_2 = 45\; 	ext{cm of Hg}$,$T_2 = -7 + 273 = 266\; 	ext{K}$.Using the relation $M_1 / M_2 = (P_1 / T_1) / (P_2 / T_2) = (P_1 T_2) / (P_2 T_1)$:$M_2 = M_1 	imes (P_2 / P_1) 	imes (T_1 / T_2) = 185 	imes (45 / 76) 	imes (300 / 266)$.$M_2 = 185 	imes 0.5921 	imes 1.1278 \approx 123.54\; 	ext{kg}$.

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