A spherical balloon of radius 3 cm containing helium gas has

Question

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.

DivineJEE · Accepted Answer

At constant temperature and number of moles

$P_1 V_1=P_2 V_2 \\$

$P_1=48 \times 10^{-3} \mathrm{bar} ; V_1=\frac{4}{3} \pi(3)^3 \\$

$V_2=\frac{4}{3} \pi(12)^3 \\$

$P_2=\frac{P_1 V_1}{V_2}=\frac{48 \times 10^{-3} \times(3)^3}{(12)^3} \\$

$=\frac{48 \times 10^{-3}}{64}=7.5 \times 10^{-4}=750 \times 10^{-6} \mathrm{bar}$

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