Question

Nicholas Mason inflated a weather balloon using just the power of his lungs. The balloon’s final radius was 1.22 m. If 642 kJ of work was done to inflate the balloon, at what net pressure was the balloon inflated?

Answer 1

As per the given question,

Final radius of the balloons R=1.22m

And total work done =642KJ

Let the initial radius of the balloons r=0

So, change in the volume of the cylinder $(\Delta V)=\dfrac{4\pi R^3}{3}-\dfrac{4\pi r^3}{3}=\dfrac{4\pi R^3}{3}-0$

$(\Delta V)=\dfrac{4\pi R^3}{3}=\dfrac{4\times 3.14\times 1.22^3}{3}m^3$

Let the Final pressure (P)=?

Now, we know that work done $(W)=P\Delta V$

$=642\times 10^3\times \dfrac{4\times 3.14\times 1.22^3}{3}=4880.70\times 10^3 p$

$=4.88\times 10^6 p$