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? (in \({kg}\))

Pick an option to check your answer.

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Answer & Solution

Correct Answer

(D) \(123.54\)

Detailed explanation

\(P{m}=\rho R T\)

\(\therefore \frac{P_{1}}{P_{2}}=\frac{\rho_{1} T_{1}}{\rho_{2} T_{2}}\)

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

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

\(\therefore M_{2} \Rightarrow \frac{45 \times 300 \times 185}{76 \times 266}=123.54 \,{kg}\)

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