Energy Transfer by Heat

Thus far, we have considered quantitatively only those interactions between a system and its
surroundings that can be classed as work. However, closed systems also can interact with
their surroundings in a way that cannot be categorized as work. for example... when
a gas in a rigid container interacts with a hot plate, the energy of the gas is increased even
though no work is done. This type of interaction is called an energy transfer by heat.
On the basis of experiment, beginning with the work of Joule in the early part of the nineteenth century, we know that energy transfers by heat are induced only as a result of a temperature difference between the system and its surroundings and occur only in the direction
of decreasing temperature. Because the underlying concept is so important in thermodynamics, this section is devoted to a further consideration of energy transfer by heat.
Sign Convention, Notation, and Heat Transfer Rate
The symbol Q denotes an amount of energy transferred across the boundary of a system in
a heat interaction with the system’s surroundings. Heat transfer into a system is taken to be
positive, and heat transfer from a system is taken as negative.
This sign convention is used throughout the book. However, as was indicated for work, it is
sometimes convenient to show the direction of energy transfer by an arrow on a sketch of
Q >0: heat transfer from the system
Q < 0: heat transfer to the system
the system. Then the heat transfer is regarded as positive in the direction of the arrow. In an
adiabatic process there is no energy transfer by heat.
The sign convention for heat transfer is just the reverse of the one adopted for work, where
a positive value for W signifies an energy transfer from the system to the surroundings. These
signs for heat and work are a legacy from engineers and scientists who were concerned mainly
with steam engines and other devices that develop a work output from an energy input by
heat transfer. For such applications, it was convenient to regard both the work developed and
the energy input by heat transfer as positive quantities.
The value of a heat transfer depends on the details of a process and not just the end states.
Thus, like work, heat is not a property, and its differential is written as Q. The amount of
energy transfer by heat for a process is given by the integral


ewline"> where the limits mean “from state 1 to state 2” and do not refer to the values of heat at those
states. As for work, the notion of “heat” at a state has no meaning, and the integral should
never be evaluated as Q2 Q1.
The net rate of heat transfer is denoted by In principle, the amount of energy transfer by heat during a period of time can be found by integrating from time t1 to time t2
 
To perform the integration, it would be necessary to know how the rate of heat transfer varies
with time.
In some cases it is convenient to use the heat flux, , which is the heat transfer rate per
unit of system surface area. The net rate of heat transfer, , is related to the heat flux by
the integral


where A represents the area on the boundary of the system where heat transfer occurs.
UNITS. The units for Q and are the same as those introduced previously for W and
respectively. The units for the heat flux are those of the heat transfer rate per unit area: kW/m2
or