Chapter 13.1, Problem 19SSC

Interpretation Introduction

Interpretation:

To develop a map showing relationship among pressure, volume and temperature of the gas.

Concept introduction:

It involves various gas laws as follows:

Boyle’s Law

Charles’ Law

Gay-Lussac’s Law

Answer to Problem 19SSC

The various relations are:

According to Boyle’s Law

$\mathrm{PV}=constant$ , keeping the temperature constant

According to Charles’ Law

$\frac{V}{T}=constant$, keeping the pressure constant

According to Gay-Lussac’s Law

$\frac{\mathrm{P}}{T}=constant$, keeping the volume constant

Where

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

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

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

Explanation of Solution

Boyle’s Law states that at constant temperature, pressure is inversely proportional to the volume for a given amount of gas.

$\mathrm{P}\propto \frac{1}{V}$

Or

$\mathrm{PV}=constant$

Charles’ Law states that at constant pressure, volume is directly proportional to the temperature for a given amount of gas.

$\mathrm{V}\propto T$

Or

$\frac{V}{T}=constant$

Gay Lussac's law states that at constant volume, pressure is directly proportional to the temperature for a given amount of gas.

$\mathrm{P}\propto T$

Or

$\frac{\mathrm{P}}{T}=constant$

Conclusion

Thus, these gas laws establish relationship between three variables pressure, temperature and volume keeping one variable constant at a time.