Chapter 13.1, Problem 16SSC

Interpretation Introduction

Interpretation:

Thevolume of a weather balloon at specific height is to be predicted.

Concept introduction:

It can be predicted with the help of combined gas law.

Answer to Problem 16SSC

The value of pressure and temperature at the final altitude are required to be known to predict its volume. Combined gas law is used to calculate this volume.

Explanation of Solution

Ideal gas equation (combined gas law) helps to calculate volume of a gas at given temperature and pressure. According to this law,

$\mathrm{PV}=nRT$

Or

$\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}$

Where

${\mathrm{P}}_1$ is initial pressure of the gas

${\mathrm{V}}_1$ is initial volume of the gas

${\mathrm{T}}_1$ is the initial temperature of the gas

${\mathrm{P}}_2$ is final pressure of the gas

${\mathrm{V}}_2$ is final volume of the gas

${\mathrm{T}}_2$ is the final temperature of the gas

As the initial pressure, temperature and volume are known, by knowing the final pressure and temperature, one can calculate volume at final stage using the formula:

$V_2=\frac{P_1{V}_1{T}_2}{P_2{T}_1}$

Conclusion

Combined gas law helps to calculate one variable out of three(pressure, volume, temperature) if two are known.