Heat

PD Image
Energy of the hot gas flame flows into the cold water in the kettle.

Heat is a form of energy that is transferred between two bodies that are in thermal contact and have different temperatures. For instance, the bodies may be two compartments of a vessel separated by a heat-conducting wall and containing a fluid of different temperature on either side of the wall. Or one body may consist of hot radiating gas and the other a kettle with cold water, as shown in the picture. Heat flows spontaneously from the higher-temperature to the lower-temperature body. The effect of this transfer of energy usually, but not always, is an increase in the temperature of the colder body and a decrease in the temperature of the hotter body.

Change of aggregation state

A vessel containing a fluid may lose or gain energy without a change in temperature when the fluid changes from one aggregation state to another. For instance, a gas condensing to a liquid does this at a certain fixed temperature (the boiling point of the liquid) and releases condensation energy. When a vessel, containing a condensing gas, loses heat to a colder body, then, as long as there is still vapor left in it, its temperature remains constant at the boiling point of the liquid, even while it is losing heat to the colder body. In a similar way, when the colder body is a vessel containing a melting solid, its temperature will remain constant while it is receiving heat from a hotter body, as long as not all solid has been molten. Only after all of the solid has been molten and the heat transport continues, the temperature of the colder body (then containing only liquid) will rise.

Units

At present the unit for the amount of heat is the same as for any form of energy. Before the equivalence of mechanical work and heat was clearly recognized, two units were used. The calorie was the amount of heat necessary to raise the temperature of one gram of water from 14.5 to 15.5 °C and the unit of mechanical work was basically defined by force times path length (in the old cgs system of units this is erg). Now there is one unit for all forms of energy, including heat. In the International System of Units (SI) it is the joule, but the British Thermal Unit and calorie are still occasionally used. The unit for the rate of heat transfer is the watt (J/s).

Equivalence of heat and work

Although heat and work are forms of energy that both obey the law of conservation of energy, they are not completely equivalent. Work can be completely converted into heat, but the converse is not true. When converting heat into work, part of the heat is not—and cannot be—converted, but flows to the body of lower temperature that is necessarily present to generate an energy flow.

Heat and temperature

The important distinction between heat and temperature (heat being a form of energy and temperature a measure of the amount of that energy present in a body) was clarified by Count Rumford, James Prescott Joule, Julius Robert Mayer, Rudolf Clausius, and others during the late 18th and 19th centuries. Also it became clear by the work of these men that heat is not an invisible and weightless fluid, named caloric, as was thought by many 18th century scientists, but a form of motion. The molecules of the hotter body are (on the average) in more rapid motion than those of the colder body. The first law of thermodynamics, discovered around the middle of the 19th century, states that the (flow of) heat is a transfer of part of the internal energy of the bodies. In the case of ideal gases, internal energy consists only of kinetic energy and it is indeed only this motional energy that is transferred when heat is exchanged between two containers with ideal gases. In the case of non-ideal gases, liquids and solids, internal energy also contains the averaged inter-particle potential energy (attraction and repulsion between molecules), which depends on temperature. So, for non-ideal gases, liquids and solids, also potential energy is transferred when heat transfer occurs.

Forms of heat

The actual transport of heat may proceed by electromagnetic radiation (as an example one may think of an electric heater where usually heat is transferred to its surroundings by infrared radiation, or of a microwave oven where heat is given off to food by microwaves), conduction (for instance through a metal wall; metals conduct heat by the aid of their almost free electrons), and convection (for instance by air flow or water circulation).

Entropy

If the two bodies exchanging heat are separated from the rest of the universe (i.e., no other heat flows than between the two bodies and no work is performed on them) then the entropy of the total system increases upon the spontaneous flow of heat. This is a consequence of the second law of thermodynamics that states that spontaneous thermodynamic processes are associated with entropy increase. In this case the increase is easy to compute when we recall that the entropy S of a system at absolute temperature T increases with:

$\Delta S={\frac {\Delta Q}{T}}$

when it receives an amount of heat ΔQ. The hotter system (2) loses heat and the colder system (1) gains it and in absolute value the quantities of heat are the same by the conservation of energy, hence

$\Delta S_{\mathrm {tot} }=\Delta S_{1}+\Delta S_{2}={\frac {\Delta Q}{T_{1}}}-{\frac {\Delta Q}{T_{2}}}>0\quad {\hbox{because}}\quad T_{2}>T_{1}.$

Here we assume that the exchange of heat is so small that the temperatures of the two bodies do not change. One can achieve this by considering a small time interval and/or very large heat reservoirs.