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A balloon carries

Question:

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

  1. $181.46 \mathrm{~kg}$

  2. $214.15 \mathrm{~kg}$

  3. $219.07 \mathrm{~kg}$

  4. $123.54 \mathrm{~kg}$

Correct Option: , 4

Solution:

$\mathrm{P}_{\mathrm{m}}=\rho \mathrm{RT}$

$\therefore \frac{P_{1}}{P_{2}}=\frac{\rho_{1} T_{1}}{\rho_{2} T_{2}}$

$\frac{\rho_{1}}{\rho_{2}} \Rightarrow \frac{P_{1} T_{2}}{P_{2} T_{1}}=\left(\frac{76}{45}\right) \times \frac{266}{300}$

$\frac{\rho_{1}}{\rho_{2}} \Rightarrow \frac{M_{1}}{M_{2}}=\frac{76 \times 266}{45 \times 300}$

$\therefore \mathrm{M}_{2} \Rightarrow \frac{45 \times 300 \times 185}{76 \times 266}=123.54 \mathrm{~kg}$

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