## 4.2 Charles’s Law

After Boyle’s Law was published by Robert Boyle in 1662, it was postulated by Jacques Charles in 1780 and confirmed in 1802 that the volume of a given mass of a gas would vary according to the **absolute temperature** of the gas. At this time, no one knew the true nature of gases.

Charles’s Law states that under the condition of constant pressure the volume of a given mass of an ideal gas is directly proportional to its absolute temperature. Put into a mathematical form, Charles’s Law becomes Equation 4.6.

#### Equation 4.6

In this equation, *V* is the volume of a fixed amount of gas in terms of either moles or mass and *T* is the absolute temperature. The linear relationship between volume and temperature is seen in Figure 4.2.

Figure 4.2 Plot of volume *V* versus absolute temperature *T* for a gas at a constant pressure

Just as we did before, Equation 4.6 can be rewritten and then used to show volumes before and after a change of temperature, which results in Equation 4.7.

#### Equation 4.7

The subscripts 1 and 2 indicate the states before and after a change. Remember, absolute temperatures must be used. As mentioned in Chapter 3, “Units of Measure,” the absolute temperature scale is measured relative from absolute zero where all motion ceases. In the Celsius temperature scale, where the freezing point of pure water is defined as zero degrees Celsius (0°C) and the boiling point of water at 1 atmosphere of pressure is defined as one hundred degrees Celsius (100°C) absolute zero would be approximately –273.15°C. For the Fahrenheit scale, with 32°F and 212°F being defined as the freezing and boiling points, respectively, absolute zero is –459.67°F. Absolute temperature is discussed in more detail in the next section.

As with Boyle’s Law, Equation 4.7 can be rewritten to give Equation 4.8.

#### Equation 4.8

Alternatively, it can be arranged as shown in Equation 4.9.