Chapter 13.1, Problem 12SSC

To determine

To Calculate:The volume of gas when the balloon reaches a height of $2100\text{m}$ .

Answer to Problem 12SSC

  $3.1\times {10}^1{\text{m}}^{\text{3}}$

Explanation of Solution

Given data:

Initial pressure, $P_1=1\text{atm = }1.01\times {10}^{5}Pa$

Final pressure, $P_2=0.82\times {10}^5\text{Pa}$

Initial volume, $V_1=25.\text{0}{\text{m}}^{\text{3}}$

Formula used:

The product of the initial volume and initial pressure is equal to the product of the volume and pressure after a change if there is constant temperature.

  $P_1{V}_1=P_2{V}_2$

Where, V represents Volume and P represents pressure

Calculation:

Final volume can be obtained by:

  $V_2=\frac{P_1{V}_1}{P_2}$

Substitute the given values in formula:

  $\begin{array}{c}{V}_2=\frac{\left(\text{1}{\text{.01×10}}^{\text{5}}\text{Pa}\right)\left(\text{25}\text{.0}{\text{m}}^{\text{3}}\right)}{\left(\text{0}{\text{.82×10}}^{\text{5}}\text{Pa}\right)}\\ \approx \text{3}{\text{.1×10}}^{\text{1}}{\text{m}}^{\text{3}}\end{array}$

Conclusion:

The volume of gas when the balloon reaches a height of $2100\text{m}$ is $3.1\times {10}^1{\text{m}}^{\text{3}}$ .