Investigating Boyle's and Charles's laws

Practical method

Aim

Investigate how the pressure of a fixed mass of gas at constant volume depends on temperature and estimate absolute zero.

Variables

Independent variable: temperature θ
Dependent variable: pressure p
Control variables: volume of gas (fixed flask); mass of gas (sealed).

Apparatus

• Round-bottomed flask sealed with a bung and short tube
• Pressure gauge (Bourdon gauge or sensor)
• Large water bath with heater
• Thermometer
• Stirrer

Method

1. Connect the flask to the pressure gauge with as short a tube as possible.
2. Submerge the flask fully in the water bath with a thermometer next to it.
3. Heat the water in steps of 20 °C. At each step, stir and wait for the pressure to stop changing, then record p and θ.
4. Plot p against θ (°C) and extrapolate the line to p = 0.
5. The intercept on the temperature axis estimates absolute zero.

Sample results

Fixed volume of air.

Analysis

p rises linearly with θ, gradient 0.366 kPa °C⁻¹. Extrapolating to p = 0 gives θ = −\(\dfrac{100.0}{0.366}\) = −273 °C: absolute zero. So p ∝ T when T is in kelvin (the pressure law). Boyle's law (pV constant at constant temperature) is investigated similarly with a syringe or oil column.

Uncertainty

The long extrapolation magnifies uncertainty in the gradient: a 2% error in the gradient changes the intercept by about 5 °C. Air in the connecting tube outside the bath stays cooler, giving a systematic error.

Errors and improvements

Risk assessment

Common mistakes

• Plotting against kelvin and then trying to find absolute zero from the intercept.
• Not waiting for equilibrium.
• Starting the axis at 0 °C so the extrapolation cannot be drawn.

Worked analysis

Gradient = \(\dfrac{129.3 - 100.0}{80}\) = 0.366 kPa °C⁻¹. Intercept: θ = −\(\dfrac{100.0}{0.366}\) = −273 °C.

Common misconception

Absolute zero is not where gas molecules simply stop being a gas; it is the temperature at which the particles have minimum kinetic energy, the zero of the kelvin scale.

Variations required by some exam boards

AQA RP8 requires Boyle's law (pV constant at constant temperature) and Charles's law (V ∝ T at constant pressure) using a capillary tube or syringe; the analysis is the same, extrapolating V to zero for Charles's law.

Some boards use a pressure sensor and data logger in place of a Bourdon gauge.