Heat and Temperature: What Is the Difference?

Difference between heat and temperature — How heat propagates in a system: The three modes of heat transfer from a pot heated on a gas flame. Conduction occurs in the transmission of heat through the metal of the pot, convection is visible in the circular movements of boiling water, and thermal radiation is represented by the heat emitted by the hot walls of the container to the environment.
Image source: astronoo.com (new window)

Scientific Summary

The article clarifies the fundamental distinction between heat and temperature in thermodynamics. Temperature is an intensive quantity measuring the average molecular agitation, proportional to the average kinetic energy of particles (E = 3/2 kT). Heat is an extensive energy transferred between systems at different temperatures, measured in joules or calories. Three modes of transfer are described: conduction (Fourier's law: Q = -k A dT/dx), convection (Newton's law: Q = h A (T₁-T₂)), and radiation (Stefan-Boltzmann law: Q = σ A (T₁⁴-T₂⁴)).

What Is the Difference Between Heat and Temperature?

Temperature measures the average agitation of the molecules in an object: the more they agitate, the higher the temperature. It is an intensive property, which does not depend on the amount of matter. Heat is energy in transfer between two objects at different temperatures, which always moves from hotter to colder. It is an extensive property, depending on the amount of matter. A good example: a cup of hot coffee has a high temperature, but it is its heat (the energy transferred to your hand) that warms you.

Differences Between Heat and Temperature

Heat and temperature are two different but closely related concepts in thermodynamics.

Temperature: Measure of Molecular Agitation

Temperature is a measure of the molecular agitation of an object, while heat is a form of energy that is transferred between two bodies at different temperatures.

Thus, temperature is an intensive quantity that depends only on the thermodynamic state of an object, while heat is an extensive quantity that depends on the amount of matter and the temperature change.

Average Thermal Agitation vs. Transferred Energy

In other words, temperature measures the average thermal agitation of the molecules in an object, while heat measures the amount of energy transferred between two objects at different temperatures.

What Is Temperature?

Temperature is a physical quantity that measures the molecular agitation of a body or system.
This thermal agitation corresponds to the random motion of molecules, which is directly related to the temperature of the body or system. More simply, this quantity can be measured in degrees Celsius (°C) or kelvins (K) using a thermometer.

Average Kinetic Energy of Particles

The equation for the thermal agitation temperature of a body corresponds to the average kinetic energy of the particles.
E = ½m v² where E is the average kinetic energy of a particle, m is its mass, and v is its average speed.

Particle Speed and Temperature

According to the kinetic theory of gases, the equation below shows that the speed of particles in a gas increases with temperature.
v = sqrt((3 * k * T) / m) where T is the temperature of the gas, k is Boltzmann's constant (1.38 x 10^-23 joules per kelvin), and m is the mass of the particle.

Proportionality Between Kinetic Energy and Temperature

The equation below shows that the average kinetic energy of the particles in a gas is proportional to the absolute temperature T. Thus, the thermal agitation temperature is directly related to the temperature of the system.
E = (3/2) * k * T where E is the kinetic energy, T is the temperature of the gas, and k is Boltzmann's constant.

What Is Heat?

Heat is a form of energy that is transferred from one system to another due to a temperature difference.
Heat is measured in joules (J) or calories (cal), with one calorie being approximately 4.184 joules. It is transferred either by conduction (direct contact), convection (contact via the movement of a fluid), or radiation (heat transfer in the form of electromagnetic waves).

Transfer by Conduction: Fourier's Law

For heat transfer by conduction, for example through a flat plate of thickness L, Fourier's law gives the amount of heat Q transferred per unit time through the plate:
Q = -k * A * (dT/dx) where k is the thermal conductivity of the plate, A is its surface area, dT/dx is the temperature gradient along the plate, and the negative sign indicates that heat is transferred from the hot region to the cold region.

Transfer by Convection: Newton's Law

For heat transfer by convection between two fluids, Newton's local heat transfer equation gives the amount of heat Q transferred per unit time and surface area:
Q = h * A * (T1 - T2) where h is the heat transfer coefficient, A is the contact surface area between the fluids, T1 and T2 are the temperatures of the two fluids, and the negative sign is omitted because heat is transferred from T1 (hotter fluid) to T2 (colder fluid).

Transfer by Radiation: Stefan-Boltzmann Law

For heat transfer by radiation between two bodies, the Stefan-Boltzmann law gives the amount of heat Q emitted per unit surface area of a black body at temperature T1 and received per unit surface area of another black body at temperature T2:
Q = σ * A * (T1^4 - T2^4) where σ is the Stefan-Boltzmann constant (σ = 5.670374419 x 10^-8 W m^-2 K^-4) and A is the surface area of the two bodies.
This law assumes that the bodies are perfect black bodies, meaning they absorb all radiation that reaches them and emit radiation that follows Planck's law, which describes the emission spectrum of electromagnetic radiation emitted by a hot body.

N.B.:
These equations are not always applicable in practice, as heat transfer conditions can be complex and often depend on many parameters, such as the geometry of the bodies, the thermal properties of the materials, the flow rate of fluids, etc.

FAQ: Everything You Need to Know About Heat and Temperature

Are Heat and Temperature the Same Thing?

No, they are fundamentally different concepts. Temperature is a measure of the average molecular agitation, an intensive property (does not depend on sample size). Heat is energy in transfer between two systems due to their temperature difference, an extensive property (depends on the amount of matter). You can have a high temperature with little heat (a spark) and a low temperature with a lot of heat (an ocean).

What Are the Units of Measurement for Heat and Temperature?

Temperature is measured in kelvins (K) (SI unit) or degrees Celsius (°C). Heat (energy) is measured in joules (J) (SI unit) or calories (cal) (1 cal ≈ 4.184 J). Kelvin is the base unit of thermodynamics, while the joule is the standard unit of energy.

How Is Heat Transferred Between Two Objects?

Heat spreads through three main modes: 1. Conduction: through direct contact, such as a spoon heating up in soup (Fourier's law). 2. Convection: via the movement of a fluid (liquid or gas), such as warm air rising. 3. Radiation: through electromagnetic waves, such as the heat from the Sun (Stefan-Boltzmann law).