Concepts & Definitions

The question

A tyre gauge reads 2.2 bar. A weather report says 1.01 bar. A vacuum pump claims −0.9 bar. And somewhere below all the thermometers in the world sits a temperature, −273.15 °C, that nothing can get below. What exactly is pressure — and why is there an absolute zero?

The map for this course

Thermodynamics is the science of energy and its transformations, and the best way to learn it is to keep one real machine in view. Ours is a modern combined-cycle power plant — the most efficient way humanity has yet found to turn fuel into electricity. Air is drawn in and compressed, fuel is burned in it, and the hot gas spins a gas turbine. Its exhaust, still at 600 °C, boils water in a heat-recovery boiler, and the steam drives a second turbine. The steam is condensed and pumped back round, and its waste heat leaves through a cooling tower.

Every chapter of the course lives somewhere in this picture.

The mapOne power plant, fourteen questions

01Concepts & Definitions 02Energy & the First Law 03Evaluating Properties 04Control Volumes 05The Second Law 06Using Entropy 07Exergy 08Vapour Power Systems 09Gas Power Systems 10Refrigeration & Heat Pumps 11Thermodynamic Relations 12Psychrometrics 13Combustion 14Chemical & Phase Equilibrium

Every lesson lives somewhere in this combined-cycle power plant: the gas turbine, the heat-recovery boiler, the steam loop, the cooling tower — and three windows on the ideas inside them. Hover a chapter to see where, or tap a part of the plant to find its chapter.

Drawing a boundary

The first move in any thermodynamic analysis is to decide what you are analysing. Draw a boundary around it; what is inside is the , everything else is the surroundings.

A closed system — a control mass — always contains the same matter. Gas trapped under a piston is the classic example. Energy can cross the boundary; mass cannot.
An open system — a control volume — has matter flowing in and out. A turbine, a pump, a jet engine. We will handle these in Lesson 4.
An isolated system exchanges nothing at all with its surroundings — not even energy.

The choice is yours, and a good choice makes a problem easy. The same steam turbine can be analysed as a control volume that steam flows through, or by following one kilogram of steam as a closed system as it passes through. Both give the same answer.

Properties and states

A is any measurable characteristic of a system — mass, volume, pressure, temperature, energy — whose value depends only on the system's present condition, not on its history. The full set of property values is its .

Properties come in two kinds. Extensive properties, like volume $V$ or energy $E$ , scale with the amount of stuff: cut the system in half and they halve. Intensive properties, like pressure and temperature, do not. Dividing an extensive property by mass makes it intensive: the specific volume $v = V/m$ (m³/kg), or the specific energy $e = E/m$ . Throughout the course, lowercase letters are per unit mass.

A change of state is a process. If the system passes through a sequence of states each of which is (very nearly) in — uniform, with nothing changing on its own — it is a , and we can draw it as a curve on a diagram. A process that ends in the state it started in is a cycle: the steam in our power plant runs a cycle about once every minute.

Pressure is a crowd of molecules

Pressure is force per unit area, $p = F/A$ . But a gas has no solid surface to push with. Where does the force come from?

From billions of molecules bouncing off the walls. Each bounce reverses a molecule's momentum; summed over every impact in a second, those reversals are a steady force. Watch it happen:

ExplorePressure is molecules hitting a wall

Molecules100

Volume (piston position)1.00 V₀

Wall temperature300 K

Measured pressure1.00 p₀from wall impacts

Ideal-gas law1.00 p₀N k T / V

Gas temperature300 Kfrom molecular speeds

Ideal-gas law here: 1.00 × 1.00 ÷ 1.00 = 1.00 p₀. With few molecules the gauge jitters: pressure is an average, and only makes sense for many molecules.

Challenges0/2

With 100 molecules at 300 K, double the pressure without adding molecules.
Heat the gas above 500 K without touching any temperature control.

A two-dimensional gas of point molecules. The gauge is not computed from a formula: it adds up the momentum delivered to the walls in every bounce, averaged over about a second. Colours show each molecule’s speed. With conducting walls the gas is held at the bath temperature; with insulated walls, pushing the piston in does work on the gas — and heats it.

The ideal-gas law, $pV = NkT$ , falls out of this picture. More molecules mean more impacts. A smaller box means each molecule returns to the wall sooner. Hotter molecules move faster, so they hit both harder and more often — and the product works out exactly proportional to temperature, as long as temperature is measured from the right zero. Hold that thought.

Absolute, gauge and vacuum

We live at the bottom of an ocean of air whose weight presses on everything with about 101 kPa — 1.013 bar. Most gauges measure pressure relative to that atmosphere, because they have the atmosphere pushing on their other side:

$p_\text{gauge} = p_\text{abs} - p_\text{atm}, \qquad p_\text{vacuum} = p_\text{atm} - p_\text{abs}.$

Thermodynamic equations always use the absolute pressure — molecules don't care what the atmosphere outside is doing. The manometer below shows the difference: a column of liquid balances the pressure difference across it, $\Delta p = \rho g \Delta h$ .

ExploreAbsolute, gauge and vacuum

Tank pressure (absolute)1.20 bar

Challenges0/2

Find one tank pressure that reads as a vacuum at sea level but positive on Everest.
Try to measure a big pressure difference with water. What goes wrong?

A U-tube manometer connects a tank (left) to the open air (right). The difference in liquid levels measures the tank’s pressure relative to the atmosphere — the gauge pressure — through Δp = ρgΔh. Change where you are, and the same tank gives a different reading.

Check your intuition

A tyre is pumped to 2.2 bar gauge at sea level and then driven up to a mountain pass at 2500 m, where the atmosphere is 0.75 bar. Ignoring temperature changes, what does the gauge read there?

Temperature and the zeroth law

We all know hot from cold, but temperature has a precise thermodynamic meaning. Put two bodies in contact and wait: energy flows from one to the other until they stop changing. They are then in thermal equilibrium, and we say they have the same temperature.

The says that if body A is in thermal equilibrium with C, and B is too, then A and B are in equilibrium with each other. It sounds obvious, but it is what makes thermometers possible: C is the thermometer, and it lets us compare A and B without ever touching them together.

Any property that changes with temperature can make a thermometer — the length of a mercury column, the resistance of a platinum wire, the voltage of a thermocouple. But they disagree with each other between their calibration points. Which one is right?

A thermometer that points to zero

The answer came from gases. Fill a rigid bulb with a gas, and its pressure rises in a straight line with temperature. Read it at the freezing and boiling points of water, draw the line, and extend it backwards to zero pressure:

ExploreEvery gas points to the same zero

Filling pressure at 0 °C1.00 bar

Bath temperature50 °C

Bulb pressure1.184 barat 50 °C

Zero-pressure intercept-272.43 °C+0.72 from −273.15

Challenges0/2

Get the intercept within 0.05 °C of −273.15 °C.
Put lines for all three gases on the chart.

A constant-volume gas thermometer: a 1-litre bulb of gas whose pressure is read at the ice point (0 °C), the steam point (100 °C) and in a bath of your choice. The straight line through the readings is extended (dashed) down to zero pressure. Real-gas effects are modelled with each gas’s second virial coefficient. Press Keep to leave a filling on the chart and try another.

Every gas, at every filling, points to the same temperature: −273.15 °C. At low enough pressure the differences between gases vanish completely. That temperature, where the extrapolated pressure of an ideal gas would vanish, is the zero of the :

$T\,(\text{K}) = t\,(°\text{C}) + 273.15.$

In Lesson 5 we will find a much deeper definition of the Kelvin scale — one that does not depend on any substance at all — and discover that it is the same scale. For now, the rule is simple: in thermodynamics, temperature is always absolute. The ideal-gas law, efficiencies and entropy all break if you use Celsius.

Estimate first

How fast does a typical nitrogen molecule in room air move, in m/s?

1101001,00010,000100,000

Drag along the line to place your guess — each tick is ten times the last.

Going deeper
Going deeper: the ideal-gas law, three ways

The same law appears in three costumes. Per molecule: $pV = NkT$ with Boltzmann's constant $k = 1.381\times10^{-23}$ J/K. Per mole: $pV = n\bar{R}T$ with the universal gas constant $\bar R = 8.314$ J/(mol·K). Per unit mass, the engineer's favourite: $pv = RT$ , where $R = \bar R / M$ depends on the gas — 287 J/(kg·K) for air, 461.5 for water vapour.

The kinetic picture explains it. A molecule of mass $m$ hitting a wall at velocity component $v_x$ delivers momentum $2mv_x$ ; summing over all molecules gives $pV = N m \overline{v_x^2} = \tfrac{1}{3}Nm\overline{v^2}$ . Comparing with $pV = NkT$ says that temperature is a measure of the average kinetic energy of molecular motion: $\tfrac{1}{2}m\overline{v^2} = \tfrac{3}{2}kT$ . At absolute zero, classical molecules would stand still.

How to solve a thermodynamics problem

Moran and Shapiro insist on a disciplined method, and it is worth adopting from day one:

Known — state briefly what is given.
Find — state what is to be determined.
Schematic and given data — sketch the system, draw the boundary, mark every flow of mass, heat and work.
Engineering model — list the assumptions: steady state? ideal gas? negligible kinetic energy?
Analysis — apply the conservation laws and property relations.
Check — are the units consistent, the magnitudes sensible, the signs right?

The engineering model is where the skill lies. Real systems are messy, and the art is knowing which effects you can safely ignore.

Recap

What to carry forward

A system is whatever is inside a boundary you choose. Closed systems trap mass; control volumes let it flow.
A state is fixed by the values of the system's properties; a process changes the state; a cycle returns to it.
Pressure is the averaged force of molecular impacts. Equations use absolute pressure; gauges usually read pressure relative to the atmosphere.
The zeroth law makes thermometers possible. Gas thermometers at low pressure all point to the same absolute zero, −273.15 °C.
In thermodynamics, temperatures are always in kelvin.

Next: energy. How do work and heat change what a system holds — and how do we keep the books?