Interactive labs
Thermodynamics workbench
Four simulations you can actually drive. Change something, watch what moves with it, and check the numbers against the equations from Unit 2. Everything here runs in your browser — nothing is recorded and nothing is sent anywhere. Looking for something more general? The 3D vectors lab covers dot and cross products, sums, and the angle between two vectors.
Ideal gas & PV work
The box on the left holds a fixed amount of monatomic gas (n = 0.10 mol of argon). Move the piston or change the temperature and watch the state point travel across the PV diagram on the right. Pick a process first and the simulation will hold the right quantity constant for you.
Particle speed scales with √T; the piston sets the volume. Colour runs blue (slow) to orange (fast).
Faint curves are isotherms. The dashed one passes through your current state. The orange trail is the path you have taken.
These three accumulate from the moment you last pressed Reset trace, and they always satisfy ΔU = Q + W. Work is integrated numerically as you drag, so it is a real −∫P dV, not a formula for one special case.
- Pick Isothermal and compress. ΔU stays at 0 and Q comes out equal and opposite to W — the gas passes the energy straight through.
- Pick Adiabatic and compress. Q stays 0 and the temperature climbs on its own. That is a diesel engine.
- Run Isochoric: the volume slider locks, no area is swept, and W stays exactly 0.
- Make a closed loop — isobaric out, isochoric down, isobaric back, isochoric up — and check that ΔU returns to 0 while W does not.
Thermal conductivity
A slab bridges a hot and a cold reservoir. The steady-state transfer rate is P = kAΔT/L — proportional to conductivity, area and temperature difference, and inversely proportional to thickness.
Dot speed and count scale with the transfer rate.
- Switch copper to fibreglass with everything else fixed. The rate drops by a factor of about 10 000 — that whole range is why insulation works at all.
- Double the thickness and the rate halves; double the area and it doubles. Thickness and area are equally strong levers, in opposite directions.
- Still air conducts worse than wood. Most insulation is mostly air — the fibres exist to stop it convecting.
Entropy
Move a fixed amount of heat between two reservoirs and watch the entropy budget. The hot side loses Q/TH, the cold side gains Q/TC, and because TC is the smaller denominator the total comes out positive — only in the hot → cold direction.
Bars above the axis are entropy gained, below it lost.
Why it happens: ways to arrange 60 particles between two halves of a box. The marker is your split.
- Switch to cold → hot. Energy is still perfectly conserved — the first law cannot tell the two directions apart. Only the sign of ΔSuniverse rules one out.
- Bring the two temperatures close together. ΔSuniverse shrinks toward zero: a transfer across a vanishing temperature difference is reversible.
- Drag the particle split to 0 or 60. Ω falls to 1 — exactly one arrangement, the lowest possible entropy, and the reason gas never spontaneously crowds into one half.
Heat transfer & calorimetry
Drop two samples into an insulated container. No energy leaves, so ΣQ = 0 and the mixture settles wherever the two mcΔT terms cancel.
Bar height and colour track temperature; bar width tracks heat capacity mc.
No phase changes. If a real mixture would cross 0 °C or 100 °C the answer here is wrong, because latent heat absorbs energy at constant temperature — see the latent heat section. The container is also treated as having zero heat capacity.
- Equal masses of water and copper. The final temperature lands far closer to the water’s start, because water’s c is about 11× larger — it dominates the average.
- Watch ΣQ. It stays at zero no matter what you change; that is the calorimetry equation.
- Lead against water is the most lopsided pairing here: c = 128 against 4186.