Question

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 ?

• A. 181.46 kg
• B. 214.15 kg.
• C. 219.07 kg
• D. 123.54 kg

Answer 1

Answer: (D)

$P _{ m }=\rho RT$
$\therefore \frac{ P _{1}}{ P _{2}}=\frac{\rho_{1} T _{1}}{\rho_{2} T _{2}}$
$\frac{\rho_{1}}{\rho_{2}} \Rightarrow \frac{P_{1} T_{2}}{P_{2} T_{1}}=\left(\frac{76}{45}\right) \times \frac{266}{300}$
$\frac{\rho_{1}}{\rho_{2}} \Rightarrow \frac{M_{1}}{M_{2}}=\frac{76 \times 266}{45 \times 300}$
$\therefore M _{2} \Rightarrow \frac{45 \times 300 \times 185}{76 \times 266}$
$=123.54 \,kg$