A balloon carries a total load of 185 kg at normal pressure and… | JEE Main 2021 (27 Aug, Shift 1)

Q57JEE Main 2021 · 27 AUG · SHIFT 1Medium

Gas Laws & Ideal Gas Equation

A balloon carries a total load of 185 kg at normal pressure and temperature of 27 $^\circ$ C. What load will the balloon carry on rising to a height at which the barometric pressure is 45 cm of Hg and the temperature is $-7^\circ$ C. Assuming the volume constant?

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Answer: (d)

At constant volume the load the balloon can carry is proportional to the air density, $\rho \propto \frac{P}{T}$ .
$\frac{W_2}{W_1} = \frac{P_2}{P_1}\cdot\frac{T_1}{T_2} = \frac{45}{76}\cdot\frac{300}{266}$ .
$W_2 = 185 \times 0.592 \times 1.128 \approx 123.54\text{ kg}$ .
So the answer is (d) 123.54 kg.

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