Charles' Law Practical Notes

Charles' Law Investigation Notes

Introduction

• Charles' Law states that at constant pressure, the volume of a fixed mass of gas is proportional to its temperature.
• The experiment is straightforward but important for understanding the relationship between volume and temperature and for determining absolute zero.

Equipment

• Capillary tube: To hold the gas (dry air).
  • The gas is trapped with a thin layer of oil or a drop of sulfuric acid.
  • The tube is closed at the bottom and open at the top to maintain constant atmospheric pressure.
• Thermometer: to measure the temperature of the water.
• Ruler: To measure the height of the gas column in the capillary tube.

Theory

• The height of the gas column is proportional to its volume because the gas is in a cylindrical tube.
• $V \propto h$
  • Where $V$ is the volume of the gas and $h$ is the height of the gas column.
• The experiment can be done by heating the gas and observing its expansion or by cooling the gas and observing its contraction.
• In this experiment, freshly boiled water is used, and the temperature and height of the gas are measured as the water cools.
• It is assumed that the gas is in thermal equilibrium with the water, so the temperature of the gas is the same as the temperature of the water.

Procedure

1. Add freshly boiled water to a beaker.
   • Be careful to avoid spills.
2. Immerse the capillary tube in the water, ensuring the water covers the entire gas column.
3. Take measurements at eye level to reduce parallax error.
4. Ensure the capillary tube is close to the ruler scale for accurate readings.
5. Record the initial temperature and height of the gas column (e.g., 95 degrees Celsius and 11.8 centimeters).
6. As the water cools, record the temperature and height at regular intervals (at least eight measurements).

Data Collection

• Collect at least eight measurements of temperature and height.
• Record the temperature in degrees Celsius and the height in centimeters.

Graph Plotting

• Plot a graph of height (cm) versus temperature (°C).

Finding Absolute Zero

1. Extrapolation Method:
   • Draw the graph by hand and extrapolate the line to find where the height (volume) is zero.
   • The temperature at this point is the experimental value for absolute zero.
   • This method is less accurate.
2. Algebraic Method:
   • Calculate the gradient of the graph.
   • Use the gradient to find the value for absolute zero algebraically.

Calculations

• Calculating the gradient:
  • $m = \frac{\Delta y}{\Delta x}$, where $m$ is the gradient, $\Delta y$ is the change in height, and $\Delta x$ is the change in temperature.

Expected Results

• The experimental value for absolute zero should be close to the true value of $-273.15$ degrees Celsius.
• Calculate the percentage error:
  • $\text{Percentage Error} = \frac{{\text{Experimental Value} - \text{Accepted Value}}}{{\text{Accepted Value}}} \times 100$

Error Analysis

• Consider the possible sources of error in the investigation:
  • Parallax error in measurements.
  • Heat loss from the water to the surroundings.
  • Assuming the gas is in thermal equilibrium with the water.
  • Impurities in the gas.