Chapter 13.1, Problem 15SSC

Interpretation Introduction

Interpretation:

The relationships between pressure, volumeand temperature for equal amount of gas is to be studied.

Concept introduction:

The relations are given by various laws:

Boyle’s Law

Charles’ Law

Gay-Lussac’s Law

Answer to Problem 15SSC

• Pressure and temperature are directly proportional to each other for a fixed amount of gas keeping the volume constant.
• Pressure is inversely proportional to volume for a fixed amount of gas at constant temperature.
• Volume is directly proportional to temperature for a fixed amount of gas at constant pressure.

Explanation of Solution

The relationships between pressure, temperature and volume are explained by the following laws:

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

For equal amount of gas,

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

$\mathrm{V}\propto T$

$\mathrm{P}\propto T$