Two objects with different temperatures can exchange energy, if they are in thermal contact.  The energy exchanged between objects because they are in thermal contact is called heat.  If two objects are in thermal contact and do not exchange heat, then they are in thermal equilibrium.


The zeroth law of thermodynamics states that two object, which are separately in thermal equilibrium with a third object, are in thermal equilibrium with each other.

Two objects in thermal equilibrium with each other are at the same temperature.

How can we heat things up?

imageAtoms in molecules and solids are held together by chemical bonds.  Chemical bonds are electromagnetic in origin, but can be modeled well by tiny springs.  Two atoms held together by a spring have an equilibrium position.  If they are pushed closer together, they repel each other.  If they are pulled farther apart, they attract each other.  If they are displaced in any way from their equilibrium position and then released, they start vibrating about their equilibrium position.  An atom can form different chemical bonds with a variety of other atoms.  Different bonds are represented by springs with different spring constants.  The stiffer the spring, the more work it takes to pull the atoms apart.  If enough work is done, then the spring is stretched too much and it breaks, i.e. the chemical bond breaks.

At room temperature, gas molecules have random translational kinetic energy associated with the motion of their center of mass and random vibrational energy and rotational kinetic energy associated with the motion about their center of mass.  Collisions continuously transfer energy between the different degrees of freedom and the average energy in each degree of freedom is the same.  If work is done on the molecules which increases their vibrational energy, the amplitude of the vibrations increases, and eventually the chemical bonds break.  Most free atoms quickly form new bonds.  If the new bonds are stronger, i.e. if the new springs are stiffer, then they do more work pulling the atom towards their new equilibrium positions than was needed to break the old bonds, and the atoms will have more kinetic energy as they pass through the equilibrium positions.  This kinetic energy is quickly shared with the other degrees of freedom, the energy of all degrees of freedom increases, i.e. the thermal energy increases.  Thermal energy is released by a chemical reaction.  The temperature increases.

To burn fuel, work must first be done to break the chemical bonds in the fuel.  This work provides the activation energy, the energy needed to start the chemical reaction.  The free atoms and molecules then bond with oxygen.  The new bonds with the oxygen atoms are much stronger than the broken bonds.  As the atoms form new bonds, they gain thermal energy.  When you strike a match, you first do work against friction to break the chemical bonds in some of the fuel on the head.  The free atoms and molecules now combine with oxygen from the air, forming stronger bonds and thus releasing thermal energy.  The random kinetic energy of these fast molecules is transferred in collisions to neighboring atoms and molecules, breaking their bonds, etc.

Heat flow

imageWhen you bring two objects of different temperature together, energy will always be transferred from the hotter to the cooler object.  The objects will exchange thermal energy, until thermal equilibrium is reached, i.e. until their temperatures are equal.  We say that heat flows from the hotter to the cooler object.  Heat is energy on the move.

Units of heat are units of energy.  The SI unit of energy is Joule.  Other often encountered units of energy are 1 Cal = 1 kcal = 4186 J, 1 cal = 4.186 J, 1 Btu = 1054 J.

Without an external agent doing work, heat will always flow from a hotter to a cooler object.  Two objects of different temperature always interact.  There are three different ways for heat to flow from one object to another.  They are conduction, convection, and radiation.


imageThe atoms in a solid vibrate about their equilibrium positions.  As they vibrate, they bump into their neighbors.  In those collisions they exchange energy with their neighbors.  If the different regions of a solid object or of several solid objects placed in contact with each other have the same temperature, then all atoms are just as likely to gain energy as to loose energy in the collisions.  Their average random kinetic energy does not change.  If, however, one region has a higher temperature than another region, then the atoms in the high temperature region will, on average, loose energy in the collisions, and the atoms in the low temperature region will, on average, gain energy.  In this way heat flows through a solid by conduction.

The stiffness of the springs (strength of the chemical bonds) determines how easily the atoms can exchange energy and therefore determines if the material is a good or bad conductor of heat.  Each atom has a nucleus, surrounded by electrons.  In a solid metal all nuclei are bound to their equilibrium positions.  But some electrons are free to move throughout the solid.  They can easily pick up kinetic energy in collisions with hot cores and loose it again in collision with cooler cores.  Since their mean free path between collisions is larger than the distance between neighboring atoms, thermal energy can move quickly through the material.  Metals are, in general, much better conductors of heat than insulators.


imageConvection transfers heat via the motion of a fluid which contains thermal energy.  In an environment where a constant gravitational force F = mg acts on every object of mass m, convection develops naturally because of changes in the fluid's density with temperature.  When a fluid, such as air or water, is in contact with a hotter object, it picks up thermal energy by conduction.  Its density decreases.  For a given volume of the fluid, the upward buoyant force equals the weight of this volume of cool fluid.  The downward force is the weight of this volume of hot fluid.  The upward force has a larger magnitude than the downward force and the volume of hot fluid rises.  Similarly, when a fluid is in contact with a colder object, it cools and sinks.  When a volume of fluid such as air or water starts to move, the surrounding fluid has to rush in to fill the void.  Otherwise large pressure differences would develop.  This sets up a convection current and the looping path that follows is a convection cell.  Since fluid cannot pile up at some point in space without creating a high-pressure area, it will flow in a closed loop.  Convection can be increased if the fluid is forced to circulate.  A fan, for example, forces the air to circulate.

Video:  Convection Current (Youtube)


imageNuclei and electrons are charged particles.  When charged particles accelerate, they emit electromagnetic radiation and loose energy.  Vibrating particles are always accelerating since their velocity is always changing.  They therefore always emit electromagnetic radiation.  Charged particles also absorb electromagnetic radiation.  When they absorb the radiation they accelerate.  Their random kinetic energy increases.  In thermal equilibrium, the amount of energy they lose to radiation equals the amount of energy they gain from radiation.  But hotter objects emit more radiation than they absorb from their cooler environment.  Radiation can therefore transport heat from a hotter to a cooler object.

Electromagnetic radiation refers to electromagnetic waves, which travel through space with the speed of light.  We classify electromagnetic waves according to their wavelength.  A graphical representation of the electromagnetic spectrum is shown in the figure below.


The visible part of the spectrum may be further subdivided according to color, with red at the long wavelength end and violet at the short wavelength end, as illustrated in the next figure.


imageHot objects emit radiation with a distribution of wavelengths.  But the average wavelength of the radiation decreases as the temperature of the object increases.  Most thermal radiation lies in the infrared region of the spectrum.  We cannot see this radiation, but we can feel it warming our skin.  Different objects emit and absorb infrared radiation at different rates.  Dark surfaces are generally good emitters.

Examples of all heat transfer processes:


When a wood stove is used to heat the air in a room, conduction, convection, and radiation play a role.


When the wood burns, chemical energy stored in the wood is converted into thermal energy of the reaction products.  By conduction, these reaction products heat the surfaces and the air they are in contact with.

imageConvection draws the hot smoke up a long black pipe and out of the room and draws fresh air into the stove.  When the smoke is in contact with inner the surface of the pipe, it heats the pipe by conduction.  Conduction also carries the thermal energy from the inner surfaces of the stove and the pipe to the outer surfaces, and heats the air close to the surfaces.  The hot air then begins to rise by convection.  Cooler air rushes in to replace the rising air, and a convection current begins to flow in a convection cell.  This distributes the warm air throughout the room.  The hot, black, outer surface of the stove is also a good emitter of infrared thermal radiation.  This thermal radiation is absorbed by the surfaces of different objects in the room.