# Gas Laws: Charles's Law

## Concepts

A significant advance in the study of gases came in the early 1800's in France. Hot air balloons were extremely popular at that time and scientists were eager to improve the performance of their balloons. Two prominent French scientists, Jacques Charles and Joseph-Louis Gay-Lussac, made detailed measurements on how the volume of a gas was affected by the temperature of the gas.

Just as Robert Boyle made efforts to keep all properties of the gas constant except for the pressure and volume, so Jacques Charles took care to keep all properties of the gas constant except for temperature and volume. The equipment used by Jacques Charles was similar to that employed by Robert Boyle. A quantity of gas was trapped in a J-shaped glass tube that was sealed at one end. This tube was immersed in a water bath; by changing the temperature of the water Charles was able to change the temperature of the gas. The pressure was held constant by adjusting the height of mercury so that the two columns of mercury had equal height, and thus the pressure was always equal to the atmospheric pressure.

Intuitively, it is expected that the volume of the gas will increase as the temperature increases. Is this relationship linear? A plot of V vs T can be used to test this hypothesis.

If a decrease in temperature results in a decrease in volume, what happens if the temperature is lowered to a point where the volume drops to zero? A negative volume is obviously impossible, so the temperature at which the volume drops to zero must, in some sense, be the lowest temperature that can be achieved. This temperature is called absolute zero.

## Experiment

### Objectives

• Determine how the volume of a gas changes with temperature for a fixed amount of gas and fixed pressure.
• Determine the value of absolute zero.

A sample of air is trapped in the closed end of the manometer. (The air has been given an artificial light green color to illustrate its presence.) The amount of mercury in the manometer has been adjusted so that the two columns of mercury have the same height, and thus the pressure of the gas equals the atmospheric pressure.

Carefully measure the height of the column of trapped air and determine the volume of the trapped gas. The inside diameter of the manometer tube is 4.000 cm. Read the temperature from the thermometer, enter the temperature and volume in the boxes provided, and plot the point on the graph.

Change the temperature of the system using the heat and cool buttons. (For the purposes of this virtual experiment, assume the manometer is immersed in a colorless medium that remains liquid over a very wide range of temperatures.) The volume of the gas will change in response to the temperature change. Carefully adjust the amount of mercury in the manometer so that the heights of the two columns of mercury are identical. Then measure the height of the column of gas and calculate the volume of the gas. Continue this process until data is obtained at at least five different temperatures.

For each pair of volume-temperature values, enter the data in the table. The point will automatically be plotted on the graph along with the line-of-best-fit.

Is the plot of V vs T linear?

At what temperature does V = 0? This temperature is absolute zero. The absolute temperature is a temperature scale in which zero corresponds with absolute zero and the size of a degree is the same as the size of a degree in the celcius scale.

Compare your value for absolute zero with the accepted value. How well do the values agree? Consider the magnitude of the "experimental" error in your measurements from this virtual experiment and how this error results in error in the value of absolute zero.

Reminders
The effective top of the left side of the manometer is at a scale reading of 1041 mm.
The tube has an inside diameter of 4.000 cm

°C

mL

T (°C)
V (mL)
Volume vs Temperature

CharlesLaw.html version 3.0
© 2001, 2014, 2023 David N. Blauch