Heat and Temperature: Two Thermal Notions Too Often Confused

Scientific abstract

This article clarifies the fundamental distinction between temperature and heat in physics. Temperature is an intensive quantity measuring the average agitation of particles (average kinetic energy proportional to 3/2 kT), expressed in kelvins (K). Heat is a transfer of thermal energy between systems in interaction, an extensive quantity expressed in joules (J), depending on the mass and the specific heat of the material (Q = m·c·ΔT). The article illustrates these concepts with examples and a table of specific heats. It emphasizes that heat is not contained in a body, but exchanged.

What is the fundamental difference between heat and temperature, and why is this distinction important?

The fundamental difference is that temperature is a measure of state (the agitation of particles), while heat is a transfer of energy between systems. Temperature is an intensive quantity: it does not depend on the amount of matter (a small and a large volume of water at 20 °C have the same temperature). Heat is an extensive quantity: it depends on the mass, the material (its specific heat) and the temperature variation (Q = m·c·ΔT). This distinction is crucial because it explains counter-intuitive phenomena: a nail heated red-hot (800 °C) contains less total thermal energy than a bucket of lukewarm water (40 °C) due to the difference in mass and heat capacity. Heat is never "contained" in a body: it is exchanged by conduction, convection or radiation, and ceases when thermal equilibrium is reached.

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Two fundamental but distinct notions

Two complementary concepts

In physics, heat and temperature are two linked but fundamentally different concepts.

Temperature measures the thermal state of a system: in other words, the average agitation of the particles that compose it.
Heat corresponds to a transfer of thermal energy between two bodies or systems in interaction; it is an energy in transit.

Temperature: an intensive quantity

Definition and measurement of temperature

Temperature is a physical measurement that indicates the degree of hotness or coldness of an object, a substance or the environment. It is directly related to the average kinetic energy of the microscopic particles (atoms or molecules) that make up matter: the faster the particles move, the higher the temperature.

Temperature is an intensive quantity: it does not depend on the size of the system (mass, volume, amount of matter); it remains constant if the system is divided into several identical parts. It is expressed in kelvins (K) in the International System.

For example, in an ideal gas, the average kinetic energy of a molecule is proportional to \(\frac{3}{2}kT\), where \(k\) is the Boltzmann constant and \(T\) the temperature. For an ambient temperature of \(T = 300\,\text{K}\), this energy is: \[ \frac{3}{2}kT = \frac{3}{2} \times 1{,}38 \times 10^{-23}\,\text{J·K}^{-1} \times 300\,\text{K} \approx 6{,}21 \times 10^{-21}\,\text{J} \] This is an extremely small energy on the macroscopic scale, but sufficient to explain the constant agitation of molecules at ambient temperature.

Thermodynamic scales: Celsius, Fahrenheit and Kelvin

The main scales are Celsius, Fahrenheit and Kelvin.

Celsius (°C): 0 °C corresponds to the freezing point of water; 100 °C corresponds to the boiling point of water (at normal atmospheric pressure).
Fahrenheit (°F): 32 °F corresponds to the freezing point of water; 212 °F corresponds to the boiling point of water.
Kelvin (K): 0 K corresponds to absolute zero (–273.15 °C), the lowest possible temperature where the thermal agitation of particles ceases.

Heat: transfer of thermal energy

Definition of heat

Heat is a form of energy in transit between two thermodynamic systems. It does not designate an intrinsic property of a body, but a quantity of energy transferred because of a temperature difference. This transfer can occur by conduction, convection or radiation, and stops when thermal equilibrium is reached. Heat is therefore a quantity linked to an interaction, and not to the state of an isolated system.

Heat: a form of energy in motion

Unlike temperature, heat is an extensive quantity (it depends on the mass and the material). It is expressed in joules (J) and can only exist during an exchange. It can be transferred by conduction (direct contact), convection (fluid movements) or radiation (electromagnetic waves).

Specific heat and heat capacity

Specific heat represents the amount of energy required to raise the temperature of 1 kg of material by 1 kelvin (or 1 degree Celsius). For specific heat, the difference between kelvin and degree Celsius is negligible, because we consider a temperature variation, not an absolute temperature.

The higher the specific heat of a material, the more energy is required to heat a given mass of that material.

Specific heat of some common materials
Material	Formula	State	Specific heat \(c\) (J·kg⁻¹·K⁻¹)
Hydrogen	H₂	Gas	\(14300\)
Water	H₂O	Liquid	\(4186\)
Ice	H₂O	Solid	\(2090\)
Aluminium	Al	Solid	\(900\)
Iron	Fe	Solid	\(449\)
Copper	Cu	Solid	\(385\)
Gold	Au	Solid	\(129\)

Reference: Handbook of Chemistry and Physics, CRC Press (2024).

Why is this reality not intuitive?

Mass and specific heat explain these counter-intuitive behaviors.

At equal mass, hydrogen is harder to heat than gold (because its specific heat is greater).
At equal volume, much more energy is required to heat gold (because its mass is much greater).

The quantity of heat required to change the temperature of a material depends on its specific heat \(\,c\,\) (in J·kg⁻¹·K⁻¹): \( Q = m \cdot c \cdot \Delta T \) where \(Q\) is the heat received, \(m\) the mass of the body, \(c\) the specific heat, and \(\Delta T\) the temperature variation.

Comparative table between heat and temperature

The following table summarizes the essential differences between heat and temperature.

Comparison between heat and temperature
Concept	Nature	SI unit	Quantity	Measurement
Temperature	Thermal state	Kelvin (K)	Intensive	Thermometer
Heat	Energy in transit	Joule (J)	Extensive	Calorimeter

Common confusion in everyday life

A frequent language error

We often say that an object "contains heat", whereas in physical rigor, heat is not contained: it is exchanged between systems. What characterizes the thermal state of a body is its temperature, while internal energy depends on its mass, its temperature and its nature. For example, a bucket of lukewarm water can have a greater total internal energy than a red-hot nail, even though its temperature is much lower.

Comparative table: temperature, mass and transferred heat

This table illustrates how temperature, mass and transferred heat vary depending on the situations.

Comparison between temperature, mass/volume and transferred heat
Example	Temperature	Mass / Volume	Transferred heat
Red-hot nail vs. bucket of lukewarm water	Very hot nail (≈800 °C), lukewarm water (≈40 °C)	Nail: very small Water: large	Total thermal energy greater in water
Two balloons of air at the same temperature	Identical (same \( T \))	Small balloon vs. large balloon	The large balloon transfers more heat
Two tanks at different pressures	Small tank: very high pressure Large tank: moderate pressure	Small volume vs. large volume	Greater transfer from the large tank

References

FAQ: Everything you need to know about Heat and Temperature

What is the fundamental difference between heat and temperature?

Temperature is a measure of the thermal state of a system, linked to the average agitation of particles (average kinetic energy). It is an intensive quantity: it does not depend on the size of the system. Heat is a transfer of thermal energy between two systems due to a temperature difference. It is an extensive quantity: it depends on the mass, the nature of the material and the temperature variation. Heat only exists during an exchange; it is not "contained" in a body.

Why does a red-hot nail (800 °C) have less thermal energy than a bucket of lukewarm water (40 °C)?

The total thermal energy depends on the mass, the specific heat of the material and the temperature. The specific heat of water is very high (4186 J·kg⁻¹·K⁻¹) and its mass is large. Even at a moderate temperature, water contains a lot of energy. The nail has a very small mass and a much lower specific heat (iron: 449 J·kg⁻¹·K⁻¹). The total energy of the bucket of water is therefore much greater than that of the nail, despite its lower temperature. It is the formula Q = m·c·ΔT that demonstrates this.

What is specific heat and why is it important?

Specific heat (c) is the amount of energy required to raise the temperature of 1 kg of a material by 1 kelvin (or 1 °C). It is expressed in J·kg⁻¹·K⁻¹. The higher it is, the more energy is required to heat the material. Water has a very high specific heat (4186 J·kg⁻¹·K⁻¹), which explains why the oceans take a long time to warm up and cool down. Hydrogen (14300 J·kg⁻¹·K⁻¹) has an even higher specific heat. Gold (129 J·kg⁻¹·K⁻¹) heats up very easily.

How is heat transferred between systems?

Heat can be transferred by three mechanisms:
• Conduction: transfer by direct contact between particles (e.g. a spoon in a hot soup).
• Convection: transfer by fluid displacement (e.g. hot air rising in a room).
• Radiation: transfer by electromagnetic waves (e.g. heat from the Sun).
The transfer stops when the two systems reach the same temperature (thermal equilibrium).

Why is temperature said to be an intensive quantity and heat an extensive quantity?

An intensive quantity does not depend on the amount of matter: if a system is divided into two identical parts, the temperature remains the same (each half has the same temperature as the whole). An extensive quantity depends on the amount of matter: if a system is divided, the thermal energy (heat exchanged or internal energy) is divided by two. Temperature is a local property; heat is a global quantity that depends on mass and material.

What is the difference between heat and internal energy?

Internal energy is a state property of a system: it is the sum of all the kinetic and potential energies of the particles that compose it. It depends on the temperature, the mass, the nature of the material and the state (solid, liquid, gaseous). Heat is a transfer of energy between systems, not a property contained. When we say that a body "gains heat", we mean that it receives energy by thermal transfer, which increases its internal energy. Heat is therefore an energy in transit.