Heat (Physics): Definition, Formula & Examples

Everyone is familiar with the concept of being too hot or too cold or feeling heat from the sun on a warm day, but what specifically does the word "heat" mean? Is it a property of something "hot?" Is it the same thing as temperature? It turns out that heat is a measurable quantity that physicists have precisely defined.

Heat is what scientists call the form of energy that is transferred between two materials of different temperature. This transfer of energy occurs because of differences in the average translational kinetic energy per molecule in the two materials. Heat flows from the material with higher temperature to the material with lower temperature until thermal equilibrium is reached.

To understand better what is happening when this energy transfer occurs, imagine the following scenario: Two different containers are filled with tiny rubber balls bouncing all around. In one of the containers, the average speed of the balls (and hence their average kinetic energy) is much larger than the average speed of the balls in the second container (though the speed of any individual ball could be anything at any point in time as so many collisions cause a continual transfer of energy between the balls.)

If you place these containers so that their sides touch, then remove the walls separating their contents, what would you expect to happen?

The balls from the first container will begin interacting with the balls from the second container. As more and more collisions between the balls occur, gradually the average speeds of the balls from both containers become the same. Some of the energy from the balls from the first container becomes transferred to the balls in the second container until this new equilibrium is reached.

This is essentially what is happening at a microscopic level when two objects of different temperature come in contact with each other. Energy from the object at a higher initial temperature is transferred in the form of heat to the object with a lower initial temperature until a final temperature at equilibrium is reached.

Temperature is a measure of average translational kinetic energy per molecule in a substance. In the balls-in-container analogy, it is a measure of the average kinetic energy per ball in a given container. On the molecular level, atoms and molecules all vibrate and jiggle around. You can't see this motion because it happens on such a small scale.

Common temperature scales are Fahrenheit, Celsius and Kelvin, with Kelvin being the scientific standard. The Fahrenheit scale is most common in the United States. On this scale, water freezes at 32 degrees and boils at 212 degrees. On the Celsius scale, which is common in most other places in the world, water freezes at 0 degrees and boils at 100 degrees.

The scientific standard, however, is the Kelvin scale. While the size of an increment on the Kelvin scale is the same as the size of a degree on the Celsius scale, its 0 value is set at a different place. Zero degrees Kelvin is equal to -273.15 degrees Celsius.

Why such an odd choice for 0? It turns out this is much less of an odd choice than the Celsius scale's zero value. 0 Kelvin is the temperature at which all molecular motion stops. It is the absolute coldest temperature theoretically possible.

In this scientific light, the Kelvin scale makes much more sense than the Celsius scale. Think about how distance is measured, for example. It would be strange to create a distance scale where the 0 value was equivalent to the 1 m mark. On such a scale, what would it mean for something to be twice the length of something else?

The total internal energy of a substance is the total of the kinetic energies of all of its molecules. It depends on the temperature of the substance (the average kinetic energy per molecule) and the total amount of the substance (the number of molecules).

Temperature and internal energy are very similar to density and mass. While both measure a related attribute of the object, the total temperature of the system is independent of the number of molecules, while internal energy can be described as the temperature times the number of molecules.

It's possible for two objects to have the same total internal energy while having entirely different temperatures. For example, a cooler object will have a lower average kinetic energy per molecule, but if the number of molecules is large, then it can still end up with the same total internal energy of an object with high temperature and fewer molecules.

A surprising result of this relationship between total internal energy and temperature is the fact that a large block of ice can end up with more energy than a lit match head, even though the match head is so hot it's on fire!

There are three main methods by which heat energy transfers from one object to another. They are conduction, convection and radiation.

‌Conduction‌ occurs when energy transfers directly between two materials in thermal contact with each other. This is the type of transfer that occurs in the rubber ball analogy described earlier in this article. When two objects are in direct contact, energy is transferred via collisions between their molecules. This energy slowly makes its way from the point of contact to the rest of the initially cooler object until thermal equilibrium is achieved.

Not all objects or substances conduct energy in this way equally well, however. Some materials, called good thermal conductors, can transfer heat energy more readily than other materials, called good thermal insulators.

You've likely had experience with such conductors and insulators in your daily life. On a cold winter morning, how does stepping barefoot on a tile floor compare to stepping barefoot on carpet? It probably seems like the carpet is somehow warmer, however this is not the case. Both floors are likely the same temperature, but the tile is a much better thermal conductor. Because of this, it causes the heat energy to leave your body much more quickly.

‌Convection‌; is a form of heat transfer that occurs in gases or fluids. Gases, and to a lesser extent, fluids, experience changes in their density with temperature. Usually the warmer they are, the less dense they are. Because of this, and because the molecules in gasses and fluids are free to move, if the bottom portion becomes warm, it will expand and hence rise to the top due to its lower density.

If you place a pan of water on the stove, for example, the water on the bottom of the pan warms up, expands and rises to the top as the cooler water sinks. The cooler water then warms, expands, and rises and so on, creating convection currents that cause the heat energy to disperse through the system via mixing of the molecules within the system (as opposed to the molecules all staying in roughly the same place as they jiggle back and forth, bouncing into each other.)

Convection is why heaters work best to warm a house if they are placed near the floor. A heater placed near the ceiling would warm the air near the ceiling, but that air would stay put.

The third form of heat transfer is ‌radiation‌. Radiation is the transfer of energy via electromagnetic waves. Objects that are warm can give off energy in the form of electromagnetic radiation. This is how heat energy from the sun reaches the Earth, for example. Once that radiation comes in contact with another object, the atoms in that object can gain energy by absorbing it.

Two different materials of the same mass will undergo different temperature changes despite having the same total energy added due to differences in a quantity called ‌specific heat capacity‌. Specific heat capacity is dependent on the material in question. You will typically look up a material's specific heat capacity in a table.

More formally, specific heat capacity of a substance is defined as the amount of heat energy that must be added per unit mass of the substance in order to raise the temperature by 1 degree Celsius. The SI units for specific heat capacity, usually denoted by ‌c‌, are

\([\text{Heat Capacity}] = \frac{\text{J}}{\text{kg}} \text{K}\)

Think about it like this: Suppose you have two different substances that weigh exactly the same and are at exactly the same temperature. The first substance has a high specific heat capacity, and the second substance has a low specific heat capacity. Now suppose you add exactly the same amount of heat energy to both of them. The first substance – the one with the higher heat capacity – will not go up as much in temperature as the second substance.

There are many factors that affect how the temperature of a substance will change when a given amount of heat energy is transferred to it. These factors include the mass of the material (a smaller mass will undergo a greater temperature change for a given amount of heat added), the specific heat capacity ‌c,‌ and the thermal conductivity.

If there is a heat source supplying power ‌P‌, then the total heat added depends on ‌P‌ and time ‌t‌. The following equation describes this total heat energy ‌Q:‌

\(Q = P \times t.\)

The rate of temperature change is another interesting factor to consider. Do objects change their temperatures at a constant rate? It turns out that the rate of change depends on the temperature difference between the object and its surroundings in combination with their thermal conductivity. Newton's law of cooling describes this change. The closer an object is to the surrounding temperature, the slower it approaches equilibrium.

The formula that relates the change in temperature to an object's mass, specific heat capacity and heat energy added or removed is as follows:

\(Q = mc \Delta T\)

This formula only applies, however, if the substance is not undergoing a phase change. When a substance is changing from solid to liquid or changing from liquid to gas, the heat added to it is put to use causing this phase change and will not result in a temperature change until the phase change is complete.

A quantity called the latent heat of fusion, denoted ‌_L_f‌, describes how much heat energy per unit mass is required to change a substance from a solid to a liquid. Just as with specific heat capacity, its value depends on the physical properties of the material in question and is often looked up in tables. The equation which relates heat energy ‌Q‌ to the mass of a material ‌m_‌ and the latent heat of fusion is:

\(Q = mL_f\)

The same thing occurs when changing from liquid to gas. In such a situation, a quantity called the latent heat of vaporization, denoted ‌_L_v_‌, describes how much energy per unit mass must be added to cause the phase change. The resulting equation is identical except for subscript:

\(Q = mL_v\)

Internal energy ‌E‌ is the total internal kinetic energy, or thermal energy, in a material. Assuming an ideal gas where any potential energy between molecules is negligible, it is given by the formula:

\(E = \frac{3}{2}nRT\)

where ‌n‌ is the number of moles, ‌T‌ is temperature in Kelvin and the universal gas constant ‌R‌ = 8.3145 J/molK. The internal energy becomes 0 J at absolute 0 K.

In thermodynamics, the relationship between changes in internal energy, heat transferred and work done on or by a system are related via:

\(\Delta E = Q – W\)

This relationship is known as the first law of thermodynamics. In essence it is a statement of conservation of energy. Thermodynamics often describes the world through another quantity – entropy – which describes the disorder and chaos that follows energy and heat.