B.3 · IB Physics
Gas laws
Squeeze, heat or add gas to a cylinder and watch the particles and the pressure respond. The gold dot on the P–V diagram always sits on the isotherm for the current temperature and amount of gas.
Predict first
Start from the default settings (V = 6.0 L, T = 300 K, n = 3.0 mol). Halve the volume to 3.0 L, keeping T and n the same. What happens to the pressure?
P = nRT ÷ V, so with n and T fixed, P ∝ 1/V. Halving V doubles P: 3.0 × 8.31 × 300 ÷ 6.0 ≈ 1250 kPa becomes 3.0 × 8.31 × 300 ÷ 3.0 ≈ 2490 kPa.
Check it in the model: Move the Volume V slider from 6.0 to 3.0 L and compare the Pressure P readout (about 1250 kPa, then 2490 kPa).
current state isotherm at the chosen T
(P in kPa, V in litres, T in kelvin)
R = 8.31 J mol⁻¹ K⁻¹
mean kinetic energy per particle = (3/2)kBT
Try this
- Start from the Boyle preset (T = 300 K, n = 3.0 mol). Halve the volume from 6.0 L to 3.0 L and check that P doubles. Where does the gold dot move on the isotherm?
- Set V = 6.0 L and T = 150 K, then raise T to 300 K and then to 450 K. Does P ÷ T stay constant? Compare the mean kinetic energy readouts.
- Keep V and T fixed and change n from 1.0 to 4.0 mol. By what factor does P change, and why do the wall-hit counts change in the same way?
Exam tip: always convert to kelvin (T/K = θ/°C + 273) before using PV = nRT or any gas-law ratio. The readout shows both, so check that doubling the Celsius value does not double the pressure.