Heat and Temperature: Two Often Confused Thermal Notions

Two fundamental but distinct notions

In physics, heat and temperature are two related 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 interacting systems, it is an energy in transit.

Temperature: an intensive quantity

Temperature is a physical measure that indicates the degree of heat or cold of an object, substance, or environment. It is directly related to the average kinetic energy of 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 \(T\) is 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 low energy on a macroscopic scale, but sufficient to explain the constant agitation of molecules at room temperature.

Thermodynamic scales: Celsius, Fahrenheit, and Kelvin

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

Heat: transfer of thermal energy

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

Heat: a form of energy in motion

Unlike temperature, heat is an extensive quantity (it depends on mass and material). It is expressed in joules (J) and can only exist during an exchange. It can be transferred by conduction (direct contacts), 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, as we consider a temperature variation, not an absolute temperature.

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

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

Why is this reality not intuitive?

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

The amount 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, \(m\) is the mass of the body, \(c\) is the specific heat, and \(\Delta T\) is the temperature change.

Comparative table between heat and temperature

Common confusion in everyday life

It is often said that an object "contains heat," whereas in physical terms, heat is not contained: it is exchanged between systems. What characterizes the thermal state of a body is its temperature, while the internal energy depends on its mass, temperature, and 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 heat transferred