Chapter 20, Problem 24A

Use Boyle’s law to calculate the pressure on the same balloon if it instead expands to twice its volume.

$P=\frac{F}{A}$

To determine

Pressure $P_2$ .

Answer to Problem 24A

The pressure $P_2=\frac{P_1}{2}$

Explanation of Solution

Given:

Initial internal pressure, $P_1$

Balloon is expanded to twice 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 expanded to twice its volume.

So, final volume is $V_2=2V_1$

On putting the give values in the formula,

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

So, the final pressure is halved.

Conclusion:

Therefore, the pressure $P_2=P_1/2$ .