Thermodynamic temperature

Key takeaways

Thermodynamic temperature belongs to physics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Thermodynamic temperature to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Thermodynamic temperature from memory before moving on to harder problems.

Reference excerpt

Thermodynamic temperature, also known as absolute temperature, is a physical quantity that measures temperature starting from absolute zero, the point at which particles have minimal thermal motion. Thermodynamic temperature is typically expressed using the Kelvin scale, on which the unit of measurement is the kelvin (unit symbol: K). This unit is the same interval as the degree Celsius, used on the Celsius scale but the scales are offset so that 0 K on the Kelvin scale corresponds to absolute zero. For comparison, a temperature of 295 K corresponds to 21.85 °C and 71.33 °F. Another absolute scale of temperature is the Rankine scale, which is based on the Fahrenheit degree interval. Historically, thermodynamic temperature was defined by Lord Kelvin in terms of a relation between the macroscopic quantities thermodynamic work and heat transfer as defined in thermodynamics, but the kelvin was redefined by international agreement in 2019 in terms of phenomena that are now understood as manifestations of the kinetic energy of free motion of particles such as atoms, molecules, and electrons.

Overview Thermodynamic temperature can be defined in purely thermodynamic terms using the Carnot cycle. Thermodynamic temperature was rigorously defined historically long before particles such as atoms, molecules, and electrons were fully understood. The International System of Units (SI) specifies the absolute scale for measuring temperature, and the unit of measure kelvin (symbol: K) for specific values along the scale. A temperature interval of one degree Celsius is the same as one kelvin. Since the 2019 revision of the SI, the kelvin has been defined in relation to the physical property underlying thermodynamic temperature: the kinetic energy of atomic free particle motion. The revision fixed the Boltzmann constant at exactly 1.380649×10−23 J⋅K−1. The property that imbues material substances with a temperature can be readily understood by examining the ideal gas law, which relates, through the Boltzmann constant, how heat energy causes precisely defined changes in the pressure and temperature of certain gases. This is because monatomic gases like helium and argon behave kinetically like freely moving perfectly elastic and spherical billiard balls that move only in a specific subset of the possible motions that can occur in matter: that comprising the three translational degrees of freedom. The translational degrees of freedom are the familiar billiard ball-like movements along the x-, y-, and z-axes of 3D space (see Fig. 1, below). This is why the noble gases all have the same heat capacity per atom and why that value is lowest of all the gases. Molecules (two or more chemically bound atoms), however, have internal structure and therefore have additional internal degrees of freedom (see Fig. 3, below), which has the effect that molecules absorb more heat energy for any given rise in temperature than do the monatomic gases. Heat energy is born in all available degrees of freedom; this is in accordance with the equipartition theorem, so all available internal degrees of freedom have the same average energy as do their three external degrees of freedom. However, the property that gives all gases their pressure, which is the net force per unit area on a container arising from gas particles recoiling off it, is a function of the kinetic energy borne in the freely moving atoms' and molecules' three translational degrees of freedom. Fixing the Boltzmann constant at a specific value had the effect of precisely establishing the magnitude of the kelvin in terms of the average kinetic behavior of the noble gases. Moreover, the starting point of the thermodynamic temperature scale, absolute zero, was reaffirmed as the point at which zero average kinetic energy remains in a sample; the only remaining particle motion being that comprising random vibrations due to zero-point energy.

Absolute zero of temperature

Temperature scales are numerical. The numerical zero of a temperature scale is not bound to the absolute zero of temperature. Nevertheless, some temperature scales have their numerical zero coincident with the absolute zero of temperature. Examples are the Kelvin temperature scale and the Rankine temperature scale. Other temperature scales have their numerical zero far from the absolute zero of temperature. Examples are the Celsius scale and the Fahrenheit scale. At the zero point of thermodynamic temperature, absolute zero, the particle constituents of matter have minimal motion and can become no colder. Absolute zero, which is a temperature of zero kelvins (0 K), precisely corresponds to −273.15 °C and −459.67 °F. Matter at absolute zero has no remaining transferable average kinetic energy and the only remaining particle motion is due to an ever-pervasive quantum mechanical phenomenon called ZPE (zero-point energy). Though the atoms in, for instance, a container of liquid helium that was precisely at absolute zero would still jostle slightly due to zero-point energy, a theoretically perfect heat engine with such helium as one of its working fluids could never transfer any net kinetic energy (heat energy) to the other working fluid and no thermodynamic work could occur. Temperature is generally expressed in absolute terms when scientifically examining temperature's interrelationships with certain other physical properties of matter such as its volume or pressure (see Gay-Lussac's law), or the wavelength of its emitted black-body radiation. Absolute temperature is also useful when calculating chemical reaction rates (see Arrhenius equation). Furthermore, absolute temperature is typically used in cryogenics and related phenomena like superconductivity, as per the following example usage: "Conveniently, tantalum's transition temperature (Tc) of 4.4924 kelvins is slightly above the 4.2221 K boiling point of helium."

Rankine scale

… excerpt ends here. Continue reading the full article.

Illustrations

Thermodynamic temperature: Figure 1 The translational motion of fundamental particles of nature such as atoms and molecules is directly related to temperature. Here, the size of helium atoms relative to their spacing is shown to scale under 1950 atmospheres of pressure. These room-temperature atoms have a certain average speed (slowed down here two trillion-fold). At any given instant however, a particular helium atom may be moving much faster than average while another may be nearly motionless. Five atoms are colored red to facilitate following their motions. This animation illustrates statistical mechanics, which is the science of how the group behavior of a large collection of microscopic objects emerges from the kinetic properties of each individual object. — Figure 1 The translational motion of fundamental particles of nature such as atoms and molecules is directly related to temperature. Here, the size of helium atoms relative to their spacing is shown to scale under 1950 atmospheres of pressure. These room-temperature atoms have a certain average speed (slowed down here two trillion-fold). At any given instant however, a particular helium atom may be moving much faster than average while another may be nearly motionless. Five atoms are colored red to facilitate following their motions. This animation illustrates statistical mechanics, which is the science of how the group behavior of a large collection of microscopic objects emerges from the kinetic properties of each individual object.

Thermodynamic temperature: Figure 2.5 This simulation illustrates an argon atom as it would appear through a 400-power optical microscope featuring a reticle graduated with 50 μm (0.05 mm) tick marks. This atom is moving with a velocity of 14.43 μm/s, which gives the atom a kinetic temperature of one-trillionth of a kelvin. The atom requires 13.9 seconds to travel 200 μm (0.2 mm). Though the atom is being invisibly jostled due to zero-point energy, its translational motion seen here comprises all its kinetic energy. — Figure 2.5 This simulation illustrates an argon atom as it would appear through a 400-power optical microscope featuring a reticle graduated with 50 μm (0.05 mm) tick marks. This atom is moving with a velocity of 14.43 μm/s, which gives the atom a kinetic temperature of one-trillionth of a kelvin. The atom requires 13.9 seconds to travel 200 μm (0.2 mm). Though the atom is being invisibly jostled due to zero-point energy, its translational motion seen here comprises all its kinetic energy.

Thermodynamic temperature: Figure 3 Molecules have internal structures because they are composed of atoms that have different ways of moving within molecules. Being able to store kinetic energy in these internal degrees of freedom contributes to a substance's specific heat capacity, or internal energy, allowing it to contain more internal energy at the same temperature. — Figure 3 Molecules have internal structures because they are composed of atoms that have different ways of moving within molecules. Being able to store kinetic energy in these internal degrees of freedom contributes to a substance's specific heat capacity, or internal energy, allowing it to contain more internal energy at the same temperature.

Worked examples

Example 1 — a first encounter with Thermodynamic temperature

Start with the simplest possible case. Write down what Thermodynamic temperature claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Thermodynamic temperature before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Thermodynamic temperature ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Thermodynamic temperature

In research: Thermodynamic temperature appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Thermodynamic temperature in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Thermodynamic temperature is common in secondary-school and first-year university syllabi. It links to neighbouring topics SI base quantities, State functions, Temperature, so understanding it makes those chapters shorter.
In everyday life: Look for Thermodynamic temperature outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study Thermodynamic temperature in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Thermodynamic temperature means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Thermodynamic temperature out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Thermodynamic temperature in simple terms?

Thermodynamic temperature, also known as absolute temperature, is a physical quantity that measures temperature starting from absolute zero, the point at which particles have minimal thermal motion. Thermodynamic temperature is typically expressed using the Kelvin scale, on which the unit of measur…

Why does Thermodynamic temperature matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Thermodynamic temperature?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Thermodynamic temperature.