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2.3 HEAT 21

2.3 Heat
2
Heat is defined in thermodynamics as the quantity of energy that flows across the
boundary between the system and surroundings because of a temperature difference
between the system and the surroundings. Heat always flows spontaneously from
regions of high temperature to regions of low temperature. Just as for work, several
important characteristics of heat are of importance:
• Heat is transitory, in that it only appears during a change in state of the system and
surroundings. Heat is not associated with the initial and final states of the system
and the surroundings.
• The net effect of heat is to change the internal energy of the system and surround-
ings in accordance with the first law. If the only change in the surroundings is a
change in temperature of a reservoir, heat has flowed between the system and the
surroundings. The quantity of heat that has flowed is directly proportional to the
change in temperature of the reservoir.
• The sign convention for heat is as follows. If the temperature of the system is raised,
q is positive; if it is lowered, q is negative. It is common usage to say that if q is pos-
itive, heat is withdrawn from the surroundings and deposited in the system. If q is
negative, heat is withdrawn from the system and deposited in the surroundings.
Defining the surroundings as the rest of the universe is impractical because it is not
Rest of universe
realistic to search through the whole universe to see if a mass has been raised or low- Thermometers
ered and if the temperature of a reservoir has changed. Experience shows that in gen-
eral only those parts of the universe close to the system interact with the system. Outer water bath
Experiments can be constructed to ensure that this is the case, as shown in Figure 2.3.
Imagine that we are interested in an exothermic chemical reaction that is carried out in Inner water bath
a rigid sealed container with diathermal walls. We define the system as consisting
solely of the reactant and product mixture. The vessel containing the system is
immersed in an inner water bath separated from an outer water bath by a container with
Sealed
rigid diathermal walls. During the reaction, heat flows out of the system (q 6 0) , and
reaction
the temperature of the inner water bath increases to T . Using an electrical heater, the vessel
f
temperature of the outer water bath is increased so that at all times, T outer = T inner .
Because of this condition, no heat flows across the boundary between the two water
T inner
baths, and because the container enclosing the inner water bath is rigid, no work flows
across this boundary. Therefore, ¢U = q + w = 0 + 0 = 0 for the composite system T outer T inner
made up of the inner water bath and everything within it. Therefore, this composite sys-
Heating coil
tem is an isolated system that does not interact with the rest of the universe. To deter-
mine q and w for the reactant and product mixture, we need to examine only the
composite system and can disregard the rest of the universe. FIGURE 2.3
To emphasize the distinction between q and w and the relationship between q, w, An isolated composite system is created
and ¢U , we discuss the two processes shown in Figure 2.4. They are each carried out in in which the surroundings to the system
an isolated system, divided into two subsystems, I and II. In both cases, system I con- of interest are limited in extent. The walls
surrounding the inner water bath are rigid.
sists solely of the liquid in the beaker, and everything else including the rigid adiabatic
walls is in system II. We refer to system I as the system and system II as the surround-
ings in the following discussion. We assume that the temperature of the liquid is well
below its boiling point so that its vapor pressure is negligibly small. This ensures that
no liquid is vaporized in the process, and the system is closed. We also assume that the
change in temperature of the system is very small. System II can be viewed as the sur-
roundings for system I and vice versa.

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Heat is perhaps the most misused term in thermodynamics as discussed by Robert Romer [“Heat is not a
Noun.” American Journal of Physics, 69 (2001), 107–109]. In common usage, it is incorrectly referred to as a
substance as in the phrase “Close the door; you’re letting the heat out!” An equally inappropriate term is heat
capacity (discussed in Section 2.5), because it implies that materials have the capacity to hold heat, rather
than the capacity to store energy. We use the terms heat flow or heat transfer to emphasize the transitory
nature of heat. However, you should not think of heat as a fluid or a substance.