A balloon has a volume of 0.09 m3 below the surface of the water (density = 103 kg/m3) at a depth of 40 m. If the temperature remains constant, what is its volume in m3 when it is at the surface where the pressure is 1×105 N/m2?

Engineering

Physics

Statics

Question

A balloon has a volume of 0.09 m³ below the surface of the water (density = 10³ kg/m³) at a depth of 40 m. If the temperature remains constant, what is its volume in m³ when it is at the surface where the pressure is 1×10⁵ N/m²?

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Pressure of gas inside the balloon is same as the pressure of surrounding. Also gas inside the balloon obeys isothermal process, then

(P₀ + ρgh) V₁ = P₀V₂

$∴ V_{2} = (1 + \frac{10^{3} \times 10 \times 40}{10^{5}}) \times 0.09 = 0.45 m^{3}$ .