Chapter 20, Problem 23A

An inflated balloon has internal pressure $P_1$. Use Boyle’s law to calculate the pressure $P_2$ when the balloon is compressed to half its volume.

To determine

Pressure $P_2$ .

Answer to Problem 23A

The pressure $P_2=2P_1$

Explanation of Solution

Given:

Initial internal pressure, $P_1$

Balloon is compressed to half its volume.

Formula Used:

From Boyle’s law, at constant temperature

  $P_1{V}_1=P_2{V}_2$

Where, $P_1$ is initial pressure, $V_1$ is initial volume, $P_2$ is final pressure and $V_2$ is final volume.

Calculation:

Let the final internal pressure be $P_2$ and initial volume be $V_1$

As, balloon is compressed to half its volume.

So, final volume is $V_2=\frac{V_1}{2}$

On putting the give values in the formula,

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

So, the pressure is doubled.

Conclusion:

Therefore, the pressure $P_2=2P_1$ .