Squeeze & Heat

Three gas laws are one law, and the law is a mechanism: molecules hitting the walls. Squeeze them, heat them, count them — and read the temperature in kelvin, because the molecules do.

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Piston 60.0 cm³
Guided investigation — ages 14–18 physics

Gas laws, measured rather than memorised

Every task asks for a written prediction first. This is the topic where the Celsius habit does the most damage, so the value is in recording what you believed before the bath told you otherwise.

1Boyle

One product that will not move

Mode: Squeeze it  ·  15 min

Predict

The gauge reads 100 kPa with the piston at 60 cm³. You push it to 20 cm³ with the bath holding 20 °C. State the new reading and explain what the molecules are doing differently.

  1. Record p and V at five piston positions between 100 and 20 cm³. Calculate pV for each and comment on the spread.
  2. Switch the graph to p against 1/V. Describe the shape and state what its gradient represents.
  3. Compare the gauge with the pressure counted from collisions. Explain why the counted value flickers and the gauge does not.
  4. Change the bath temperature and repeat step 1. Deduce what pV depends on.
2Charles

Where zero really is

Modes: Heat it, Seal it  ·  20 min

Predict

A free piston sits at 50 cm³ with the bath at 20 °C. The bath is heated to 40 °C. State the new volume, and say whether it doubled.

  1. In Heat it, record V at 0, 25, 50, 75 and 100 °C. Plot V against θ in °C on paper and extend the line to V = 0. Record the intercept.
  2. Switch the axis to kelvin. State the intercept now and explain why V / T is a constant only on this scale.
  3. In Seal it, repeat with p. Compare the two intercepts and comment on what absolute zero means for the molecules.
  4. Outline how you would find absolute zero in the lab with a sealed flask, a water bath and a pressure sensor, and what limits the precision.
3Ideal & real

One constant, then its limits

Modes: Count it, Where it bends  ·  25 min

Predict

Two cylinders at the same p, V and T, one of helium and one of carbon dioxide. Which contains more molecules? Which contains faster ones?

  1. In Count it, set p, V, T, n to anything and calculate pV / nT. Change each one in turn. State what you find.
  2. Switch between the three gases. Record what changes on the panel and what does not, and explain the r.m.s. speeds with √(3RT/M).
  3. In Where it bends, read Z for CO&sub2; at 5, 10 and 20 MPa at 320 K. Describe the trend and identify which correction dominates at each pressure.
  4. Repeat for helium. Explain why its Z never drops below 1 at these temperatures.
  5. Discuss whether the ideal gas law is a law or a model, using the numbers you recorded.
The modelIdeal gas, pV = nRT with R = 8.314 J mol⁻¹ K⁻¹, exact in every readout. The real-gas mode uses van der Waals constants: N&sub2; a = 0.137, b = 3.87×10⁻⁵; He a = 0.00346, b = 2.38×10⁻⁵; CO&sub2; a = 0.364, b = 4.27×10⁻⁵ (SI).
The moleculesA two-dimensional model with speeds drawn from the Maxwell distribution and rescaled with √T. The collision-counted pressure is calibrated once to the gauge and thereafter tracks n, V and T on its own. It is illustrative; the gauge is the law.
The apparatusA 2.50 cm bore cylinder, so 1 kg on the piston adds 20.0 kPa. Bath 250–450 K. Atmospheric pressure 101.3 kPa.
UnitsSI throughout. Pressures in kPa (MPa in the real-gas mode), volumes in cm³, temperature in kelvin with the Celsius equivalent alongside.