Boyle's and Charles's Laws

Part 1: Boyle's Law

Boyle's Law states that the pressure $P$ of a gas is inversely proportional to its volume $V$ when temperature is constant. Mathematically:

$$P \propto \frac{1}{V} \quad \Rightarrow \quad PV = \text{constant}$$

Equipment

• Stand and clamp: To hold the apparatus securely.
• Syringe: To contain a fixed amount of air.
• Rubber tubing and pinch clip: To seal the syringe and prevent air escape.
• String: To suspend weights from the syringe.
• 100g masses with holder: For applying force to the syringe plunger.

Graphs and Calculations

1. Calculate Pressure:

• Calculate the force $F$ exerted by each mass $m$ using $F = mg$.
• Compute the pressure $P$ exerted by this force on the gas:

$$P = \frac{F}{A}$$

• Subtract standard atmospheric pressure (101 kPa) to obtain the pressure due to the applied masses alone.

2. Graph of $\frac{1}{V}$ vs. $P$:

• Plot $\frac{1}{V}$ against $P$ and draw a line of best fit. The linear relationship confirms Boyle's Law.

Improvements and Notes

• Avoid Distortion: Ensure the clamp does not deform the syringe, as this affects volume measurements.
• Lubricate the Plunger: To avoid sticking, which could lead to inaccurate volume readings.

Part 2: Charles's Law

Charles's Law states that the volume $V$ of a gas is directly proportional to its absolute temperature $\theta$ when pressure is constant. Mathematically:

$$V \propto \theta \quad \Rightarrow \quad \frac{V}{\theta} = \text{constant}$$

Equipment

• Capillary tube (sealed at one end): Contains the air sample.
• Sulfuric acid: Used to trap the air sample in the capillary tube.
• 2-litre beaker: For heating the water.
• Thermometer: To measure the temperature of water.
• Kettle: To heat the water.
• 30 cm ruler: For measuring the length of the air column in the capillary tube.

Method

1. Setup:

• Place the capillary tube in the beaker with the open end above the water.
• Pour hot water from the kettle into the beaker until the air sample in the tube is fully covered.

2. Heat and Measure Volume:

• Stir the water and record its temperature $\theta$ and the length $l$ of the trapped air column.
• Allow the water to cool by 5°C, and repeat measurements of $\theta$ and $l$ until reaching room temperature.

Graphs and Calculations

1. Graph of $l$ vs. $\theta$:

• Plot length $l$ of the air column against temperature $\theta$ and draw a line of best fit.
• The gradient $m$ and intercept $c$ allow calculation of absolute zero. Using the equation:

$$l = m\theta + c$$

Absolute zero can be estimated by setting $l = 0$ giving:

$$\theta_0 = -\frac{c}{m}$$

Safety

• Chemical Handling: Wear safety goggles to avoid eye contact with sulfuric acid.
• Hot Water: Take care with boiling water to avoid burns.

Improvements and Notes

• Chemical Purity: Ensure the capillary tube is free from any contaminants that may react with sulfuric acid.
• Accurate Measurements: The sulfuric acid thread must be fully intact to accurately trap the air column.