Required practicals › Boyle's law and Charles's law

REQUIRED PRACTICAL 8

Boyle's law and Charles's law

Investigating how the pressure of a fixed mass of gas varies with volume at constant temperature, and how volume varies with temperature at constant pressure.

What you are trying to do

Test Boyle's law by compressing a fixed mass of gas at constant temperature, and Charles's law by warming one at constant pressure.

Apparatus

  • Boyle's law: a sealed column of trapped air with an oil piston, pressure gauge and pump (the standard Boyle's law apparatus)
  • Charles's law: a capillary tube of air sealed by a bead of concentrated sulfuric acid or oil, alongside a thermometer in a water bath
  • Beaker, heater and stirrer for the bath; a ruler fixed to the capillary tube

Variables

  • Independent: the pressure (Boyle); the temperature (Charles)
  • Dependent: the volume of the trapped air, read as a column length
  • Control: the mass of trapped gas in both parts; the temperature (Boyle); the pressure, atmospheric throughout (Charles)

Method

  1. Boyle: raise the pressure in small steps. After each step, wait before reading the volume: compression warms the gas, and the law you are testing holds at constant temperature only.
Boyle's law: at constant temperature the pressure-volume curve is a hyperbola, and pV is the same number everywhere on itVppV = kpV = kpV = kconstant temperaturehalve the volume, double the pressure
FIG. 1What the readings should trace: pressure and volume in inverse proportion, a curve that straightens when p is plotted against 1/V.
  1. Read the volume (or column length, for a uniform bore) at five or more pressures, going up and coming back down to check nothing leaked.
  2. Charles: heat the water bath gently, stirring throughout, and read the trapped column's length at a series of temperatures as it expands under the constant weight of the bead and atmosphere.
Every gas line, extrapolated, hits the same temperature: minus 273 degrees Celsius, absolute zeroθ / °CV−273 °C0 °Cdifferent gases, different lines,one shared intercept
FIG. 2The Charles's law payoff: volume falls linearly with cooling, and every gas line aims at the same temperature, absolute zero.

Analysis

  1. Boyle: plot p against 1/V. A straight line through the origin is the law; equivalently every row's pV product is the same number.
  2. Charles: plot V against temperature in °C. The line is straight, and extrapolating it backward to V = 0 estimates absolute zero; with kelvin on the axis the line passes through the origin.

A worked set of readings: Boyle's law

Trapped air at constant room temperature:

p / kPaV / cm³pV / kPa cm³
10024024000
12020024000
15016024000
20012024000
24010024000

The product pV is 24000 kPa cm³ in every row, and p against 1/V is a straight line through the origin: Boyle's law on one page.

A worked set of readings: Charles's law

The same fixed mass of air warming at atmospheric pressure:

θ / °CV / cm³
060.0
2064.4
4068.8
6073.2
8077.6
10082.0

The line has gradient 0.220 cm³ per °C and reaches V = 0 at θ = -273 °C: the extrapolation lands on absolute zero.

Where the uncertainty comes from

  • Temperature control (Boyle): The whole experiment rests on isothermal changes: small steps, patient waits, and the up-and-down check.
  • Reading a column: A uniform bore turns volume into length; parallax at the meniscus or bead is the main reading error.
  • Thermometer and bath: Stir constantly and give the trapped air time to reach the bath's temperature; the thermometer reads the water, not the air, unless you let them agree.
  • The extrapolation: Absolute zero sits far outside the measured range, so a small gradient error moves the intercept a long way. Quote it as an estimate.

What earns the marks

  • Give the reason for slow, stepped pressure changes: keeping the compression isothermal.
  • Linearise: p against 1/V, and V against T. Both gradient meanings get asked.
  • Stir the bath, and wait for thermal equilibrium before reading.
  • The extrapolation to −273 °C is the expected finish of the Charles analysis; know that all gases point at the same intercept.

Safety

Pressurised glassware wants safety spectacles, and the Boyle apparatus should not be pumped beyond its rated pressure. Hot water and heaters need the usual respect, and an acid-sealed capillary is handled by the teacher.

Method and analysis here follow the standard approach; your school may vary the apparatus. Always follow your teacher’s risk assessment in the lab.