Question

A balloon carries a total load of $185kg$ 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 $45cm$ 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)

$P_m=\rho RT$
$\therefore \frac{P_1}{P_2}=\frac{{\rho }_1{T}_1}{{\rho }_2{T}_2}$
$\frac{{\rho }_1}{{\rho }_2}\Rightarrow \frac{P_1{T}_2}{P_2{T}_1}=\left(\frac{76}{45}\right)\times \frac{266}{300}$
$\frac{{\rho }_1}{{\rho }_2}\Rightarrow \frac{M_1}{M_2}=\frac{76\times 266}{45\times 300}$
$\therefore M_2\Rightarrow \frac{45\times 300\times 185}{76\times 266}$
$=123.54kg$