A spherical balloon of radius 3 cm containing helium gas has a pressure of \(48 \times 10^{-3}\) bar. At the same temperature, the pressure, of a spherical balloon of radius 12 cm containing the same amount of gas will be ______ \(\times 10^{-6}\) bar.
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Correct Answer: 750
Solution and Explanation
\(V = \frac{4}{3}\pi r^3 \propto r^3\), so \(V_2/V_1 = (12/3)^3 = 4^3 = 64\).
\(P_2 = P_1 \times \dfrac{V_1}{V_2} = \dfrac{48 \times 10^{-3}}{64} = 0.75 \times 10^{-3}\) bar = \(750 \times 10^{-6}\) bar.
Answer: 750
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