Question

A hot-air balloon has a volume of 2500 m3 . The balloon fabric (the envelope) weighs 860 N . The basket with gear and full propane tanks weighs 1200 N .
a) If the balloon can barely lift an additional 3400 N of passengers, breakfast, and champagne when the outside air density is 1.23kg/m3, what is the average density of the heated gases in the envelope?

Answer 1

Answer:

1.007 kg/m³

Explanation:

Given that:

volume = 2500 m³

density of air $\rho = 1.23 \ kg/m^3$

weight of air displaced = $V \times \rho \times g$

= 2500 × 1.23 × 9.81

= 30165.75 N

weight of the ballon fabric = 860 N; &

The propane weight = 1200 N

The passenger additional weight = 3400 N

weight of the heated gas will be = V × d × g

= 2500 × d  9.81

= 24525 d

For floating

The weight of air displaced is less than 30165.75

∴ 860 + 1200 + 3400 + 24525 d = 30165.75

5460 + 24525 d = 30165.75

24525 d = 24705.75

d = 24705.75  / 24525

d = 1.007 kg/m³

Hence, the average density of the heated gas = 1.007 kg/m³