Question

A weather balloon near sea level (101,377 Pa, 298.56 K) has a volume of 270.83 ft3 (cubed). If it is launched and ascends to a height of 105,200 feet (857.06 Pa, 227.85 K) before bursting. What was its final volume, in feet cubed?

Answer 1

Final volume = 24448 ft³

Explanation

According to ideal gas law,

(P₁ * V₁) / (T₁) = (P₂ * V₂) / (T₂)

where P₁ = initial pressure = 101377 Pa

V₁ = initial volume = 270.83 ft³

T₁ = initial temperature = 298.56 K

P₂ = final pressure = 857.06 Pa

V₂ = final volume

T₂ = final temperature = 227.85 K

Substituting the values,

[(101377 Pa) * (270.83 ft³)] / (298.56 K) = [(857.06 Pa) * (V₂)] / (227.85 K)

V₂ = (270.83 ft³) * (101377 Pa / 857.06 Pa) * (227.85 K / 298.56 K)

V₂ = (270.83 ft³) * (118.2846) * (0.76316)

V₂ = 24447.95 ft³