Question

A spherical balloon of radius $3cm$ containing helium gas has a pressure of $48\times 10^{-3}$ bar. At the same temperature, the pressure, of a spherical balloon of radius $12cm$ containing the same amount of gas will be ___$\times 10^{-6}$ bar

Answer 1

Answer: 750.00

As in both baloon amount of gas taken and temperature is same.

$\therefore P_1{V}_1=P_2{V}_2$ can be applied

$48\times 10^{-3}\times \frac{4}{3}\pi (3{)}^3=P_2\times \frac{4}{3}\pi (12{)}^3$

$48\times 10^{-3}\times 3^3=P_2\times \left(3^3\times 4^3\right)$

$\frac{48}{64}\times 10^{-3}bar=P_2$

$\left(\frac{48}{64}\times 1000\right)\times 10^{-6}bar=P_2$