Chapter 20, Problem 15A

When you squeeze an air-filled toy balloon to half size, how does the air pressure inside change?

To determine

The change in the air pressure inside balloon.

Answer to Problem 15A

The air pressure inside balloon is doubled, when the air inside the air balloon is squeeze to half.

Explanation of Solution

Given:

Consider a balloon filled with air. Later on, the air inside the air balloon is squeezed to half.

Formula used:

The relation between the pressure and volume of the air inside an air balloon is,

  $P_1{V}_1=P_2{V}_2$

Here, $P_1$ and $P_2$ are the initial and final pressure inside the balloon, $V_1$ and $V_2$ are the initial and final volume of the air inside the balloon.

Calculation:

Consider a balloon filled with air,

Consider that initially the volume and pressure inside the air balloon is denoted by $V_1$ and $P_1$ respectively.

Assume that the air inside the balloon is squeeze to half that means the volume of the air balloon is reduced to half.

The final volume of the air in the balloon is $V_2=\frac{1}{2}{V}_1$ .

Consider the pressure inside the air balloon when the air inside the air balloon is squeeze to half is denoted by $P_2$ .

The final pressure $\left(P_2\right)$ inside the air balloon is,

  $\begin{array}{l}{P}_1{V}_1=P_2{V}_2\\ P_1{V}_1=P_2\left(\frac{1}{2}{V}_1\right)\\ P_2=\frac{2P_1{V}_1}{V_1}\\ P_2=2P_1\end{array}$

The final pressure inside the air balloon is twice the initial pressure inside the air balloon.

Conclusion:

Thus, the air pressure inside balloon is doubled, when the air inside the air balloon is squeeze to half.