Chapter 14, Problem 52R

To determine

The new volume of the balloon.

Answer to Problem 52R

The new volume of the balloon is $48.19\text{L}$ .

Explanation of Solution

Given info:

Initial volume of the balloon, $V_1=25\text{L}$

Initial pressure of the balloon, $P_1=98.7\text{kPa}$

Final pressure of the balloon, $P_2=51.2\text{kPa}$

Formula Used:

Write the expression to calculate the new volume of the balloon using Boyles’s law.

  $\begin{array}{l}\frac{P_1}{V_2}=\frac{P_2}{V_1}\\ V_2=\frac{P_1{V}_1}{P_2}\end{array}$

Calculation:

Substitute all the values in the above expression.

  $\begin{array}{c}{V}_2=\frac{\left(98.7\text{kPa}\right)\left(25\text{L}\right)}{51.2\text{kPa}}\\ =48.19\text{L}\end{array}$

Conclusion:

Thus, the new volume of the balloon is $48.19\text{L}$ .