Assume that for every increase in height of 1 m, pressure secreases by 10 mm Hg. Initially, an experimental air ballon of miximum 200 L capacity has 150 L air at 1 atm at sea-level. At what height, the balloon is expected to burst ?

Options

A. 15 m above sea-level
B. 19 m above sea-level
C. 10 m above sea-level
D. 20 m above sea-level

Answer

D

Explanation

`V_(1) = 150 L, P_(1) = P mm Hg`
`V_(2) = 200 L, P_(2) = (P - 10 x) mm Hg`
`P_(1)V_(1) = P_(2)V_(2)`
`150 xx P = 200 xx (P - 10 x)`
`150 P = 200 P - 2000 x`
`2000 x = 50 P`
`x = (1)/(40) P = (760)/(40) = 19 m`
The balloon will after it attains a height of more than 19 m
Thus at 20 m balloon will burst