Question

Calculate the minimum number of balloons each of volume 82.1 L required to lift a mass of 1 kg to a height of 831 m.

Given: molar mass of air = 29 g/mol, the temperature is constant at 290 K and mass of each balloon is 40 g.

[Use e${}^{-01}$ = 0.9, pressure at sea level = 1 atm, acceleration due to gravity (g) = 10 m/s${}^2$]

• A. 10
• B. 20
• C. 25
• D. 50

Answer 1

The correct option is B 20

Density of air at sea level:

d${}_0$ = $\frac{29\times 1}{0.0821\times 290}$ = $\frac{1}{0.821}$ g/L

density at 831 m = d=d${}_o$e${}^{-Mgh/RT}$
= $\frac{1}{0.821}\times e^{\left(\frac{29\times {10}^{-8}\times 10\times 831}{8.31\times 2.90}\right)}$

$\Rightarrow \frac{1}{0.821}\times e^{-0.1}=\frac{9}{0.821}$ g/L

Let $x$ be number of ballons

10${}^3$ $\times$ g + $x$ $\times$ 40 g= $\frac{0.9}{0.0821}$ $\times$ 8.21 $\times$ g $\times$ $x$

$\Rightarrow$ x = 20 balloons

Hence, the correct option is $\text{B}$