Thermodynamics · ThermoLab

Thermodynamics Workstation

On the bench is a glass cylinder holding a fixed mass of gas. The small balls inside are magnified gas molecules: the warmer the colour, the faster they move.

The brass piston slides up and down. The handwheel above drives it through a lead screw; open the half-nut and the piston floats freely. The hot plate under the cylinder can heat or cool; the pressure gauge on the right and the thermometer on the left read out all the time.

The two screens on the console slope plot live graphs, and you can push or pull the levers on either side with the mouse. Press “Next stop” below to meet each part in turn.

Molecular Motion and Temperature

Gas molecules are in ceaseless random motion, colliding with each other and hitting the walls. Every molecule has a different speed, and it changes with each collision.

The left screen shows the speed distribution right now: many in the middle, few at either end. The white line is the Maxwell distribution. Push the left lever forward to heat: the molecules speed up and turn warmer, and the curve gets lower and wider with its peak moving right.

Temperature is a measure of the mean kinetic energy of the molecules: the higher the temperature, the more vigorous the thermal motion. The piston is locked here, so only the temperature changes.

Where Gas Pressure Comes From

Zoom in under the piston: every small flash is a molecule hitting the piston and bouncing back. One molecule hits only now and then, but huge numbers of molecules hitting frequently and continuously push on the piston with a steady, even force — that is gas pressure.

The left screen counts the impacts per second and the pressure worked out from their momentum. Try:

· Double the molecules (same volume, twice the number density): impacts and pressure both double;

· Raise the temperature: faster molecules hit harder and more often, so the pressure rises too.

Gas pressure depends on the number density of molecules and their mean kinetic energy.

Boyle's Law

A constant-temperature water bath now surrounds the cylinder, so the gas temperature stays the same. Move the right lever (it drives the handwheel) to push or pull the piston slowly, and watch the gauge and the left screen.

Halve the volume and the pressure doubles; double the volume and it halves. For a fixed mass of gas at constant temperature, pressure is inversely proportional to volume:

pV = C or p₁V₁ = p₂V₂

On a p–V graph this is a hyperbola (an isotherm); plotted as p against 1/V it becomes a straight line through the origin (right screen). Change the water temperature to get another isotherm — the hotter, the farther it lies from the origin.

Turn the handwheel too fast and the gas cannot exchange heat with the water in time: its temperature rises briefly and the points leave the isotherm.

Constant-Pressure Law (Charles's Law)

With the half-nut open the piston floats freely: the gas pressure always equals atmospheric pressure plus the pressure due to the piston's weight, so it stays constant.

Heat it and the expanding gas pushes the piston up; cool it and the piston sinks. For a fixed mass of gas at constant pressure, volume is proportional to absolute temperature:

V / T = C or V₁/T₁ = V₂/T₂

The V–T graph on the left screen is a straight line. Extend it to lower temperatures and it meets the axis at 0 K (−273.15 °C) — this is where the zero of the absolute temperature scale comes from.

Constant-Volume Law (Gay-Lussac's Law)

Lock the piston (red clamp) and the gas volume stays constant. Heat it: the thermometer and pressure-gauge needles climb together.

For a fixed mass of gas at constant volume, pressure is proportional to absolute temperature:

p / T = C or p₁/T₁ = p₂/T₂

The p–T graph on the left screen is again a straight line whose extension passes through 0 K. Microscopically: at constant volume the number density does not change; a higher temperature means a larger mean kinetic energy, so the molecules hit the walls harder and the pressure rises.

That is why tyres should not be pumped too hard in summer, and why a sealed can left in the sun can burst.

Work and Internal Energy

Fire syringe: put a small tuft of nitrocellulose cotton at the bottom of a thick-walled glass tube and push the piston down quickly — the cotton bursts into flame. The piston does work on the air in the tube; the air has no time to lose heat, so its internal energy and temperature shoot up past the ignition point of the cotton.

Push it down slowly instead: the same compression, but the heat leaks away as you go, the temperature stays low and the cotton does not light.

Popping cork: pump air into the bottle. The instant the cork pops, the gas inside expands and does work on its surroundings; its internal energy and temperature drop, and water vapour condenses into tiny droplets — a white mist appears in the bottle.

Both doing work and heat transfer can change an object's internal energy. Work done on an object increases its internal energy; work done by the object decreases it.

The First Law of Thermodynamics

The increase ΔU in the internal energy of a thermodynamic system equals the heat Q transferred to it plus the work W done on it:

ΔU = Q + W

The three bars on the right screen add up from the moment you press “Zero”. Sign convention: Q is positive when heat is absorbed and negative when released; W is positive when work is done on the gas and negative when the gas does work. For an ideal gas the internal energy depends only on temperature.

· Adiabatic (insulating jacket): Q = 0. Compressing gives W > 0, so the internal energy and temperature rise; expanding cools the gas.

· Isothermal (water bath): ΔU = 0. All the work done on the gas leaves as heat into the water.

· Isobaric: part of the heat absorbed raises the internal energy and part is used to do work.

· Isochoric: W = 0, so all the heat absorbed becomes internal energy.

Four-stroke petrol engine

This is a cut-away single-cylinder four-stroke petrol engine. The crankshaft turns twice and the piston goes up and down twice to complete one working cycle:

① Intake: the intake valve opens and the descending piston draws in a mixture of petrol and air; ② Compression: both valves close and the rising piston compresses the mixture — mechanical energy becomes internal energy; ③ Power: the spark plug fires and the burning gas expands violently, driving the piston down — internal energy becomes mechanical energy; this is the only stroke that does work; ④ Exhaust: the exhaust valve opens and the rising piston pushes out the burnt gas.

The other three strokes are carried by the flywheel's inertia. The left screen shows the matching ideal cycle (the Otto cycle): the area it encloses is the net work done in each cycle. Raise the compression ratio and the efficiency η = 1 − 1/rγ−1 goes up.

Switch to the racing V8: two banks of 4 cylinders fire in the order 1-8-4-3-6-5-7-2, so a cylinder fires every 90° of crank rotation and two cylinders are pushing the crankshaft at any moment. The right screen compares the torque of the two engines: the single cylinder swings wildly within each cycle and leans on its flywheel most of the time, while the V8's torque is almost a flat line — that is why multi-cylinder engines run so smoothly.

Heat-Engine Efficiency and the Carnot Cycle

A heat engine takes heat Q₁ from a hot reservoir, turns part of it into work W and gives the rest, Q₂, to a cold reservoir. Its efficiency is η = W / Q₁.

The slide under the cylinder brings up in turn: copper (hot reservoir) → white ceramic (insulator) → blue aluminium (cold reservoir) → ceramic again. The gas goes through four processes: isothermal expansion (absorbing heat from the hot reservoir) → adiabatic expansion (cooling to T₂) → isothermal compression (releasing heat to the cold reservoir) → adiabatic compression (back to T₁).

This is the Carnot cycle. Its efficiency depends only on the two reservoir temperatures:

η = 1 − T₂ / T₁

No heat engine working between these two temperatures can beat it, and as long as T₂ > 0 the efficiency is always below 100%.

The Second Law of Thermodynamics

Pull out the partition and the gas on the left quickly fills the whole box. The reverse — every molecule wandering back to the left by itself — has never been seen. Press “Rewind” and you are watching exactly that “impossible” process.

The reason is probability: each molecule has a 1/2 chance of being on the left, so the chance that all N are on the left at once is (1/2)N. With 4 molecules it happens now and then; with 200 it is so unlikely you would not see it in the age of the universe.

Put a hot and a cold copper block in contact: heat flows from hot to cold until they reach the same temperature. It never happens by itself that the cold one gets colder and the hot one hotter.

Second law of thermodynamics: heat cannot flow by itself from a colder body to a hotter one (Clausius statement); it is impossible to take heat from a single reservoir and turn it completely into work with no other effect (Kelvin statement). All macroscopic natural processes involving heat are irreversible.

Sandbox

Every control is open: the piston can float freely, be driven by the handwheel or be locked; use the hot plate, the water bath or the insulating jacket; choose a monatomic or diatomic gas.

Try designing a cycle: heat at constant volume, expand at constant pressure, cool at constant volume, then compress at constant pressure. Look at the area enclosed on the p–V graph and the work totalled on the right screen.

Compare monatomic and diatomic gases: for the same adiabatic compression, which one heats up more? Why?