The thermodynamics textbook I use claims the following:

"Heat and Work are directional quantities, and thus the complete description of a heat or work interaction requires the specification of both magnitude and direction"

This doesn't seem right to me. I've always learned that work is a scalar, so why does my textbook claim it is a vector?

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    $\begingroup$ For example, the work associated with an electrical source, over some period of time, can be positive (net work is done by the source) or negative (net work is done on the source) so it is a signed quantity but I think, like dmckee, direction is misleading. $\endgroup$ – Alfred Centauri Oct 15 '17 at 1:41
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    $\begingroup$ That's a very poorly worded, misleading statement. I'd say it's just wrong. I'd have a hard time trusting anything else in that textbook. $\endgroup$ – garyp Oct 15 '17 at 1:45
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    $\begingroup$ Mind telling us which book it is? $\endgroup$ – Sayan Mandal Oct 15 '17 at 2:51
  • $\begingroup$ Well technically for Work at least, it can be viewed as a 1-dimensional vector and this is actually somewhat appropriate as we only ever care about differences in energy. However, this doesn't seem to be the point the textbook is trying to make. I agree with others that this is either very poorly worded or just wrong. $\endgroup$ – Derek Elkins Oct 15 '17 at 3:43
  • $\begingroup$ If an insult is directed at someone why is it not a vector? $\endgroup$ – Mehrdad Oct 15 '17 at 10:21

Your source is taking an atrocious verbal shortcut. Heat and work are transfers—meaning that they have a origin and a destination—but they are adamantly scalars and not 'directional quantities'.

In particular, such transfers can have very ill-defined starting or ending locations and still be valid. Consider the case of energy transfer to a system of atoms with non-zero magnetic moments by the varying of an externally imposed magnetic field (magnetic work). Where did the energy come from? Well, we didn't have to say. Presumably it came from an electrical source of some kind or another, but it might also have come from mechanical energy used to move a permanent magnet instead.


The quoted portion from the textbook is valid. And so are the responses to the question. Cengel and co didn't call heat and work vectors. They called them "directional quantities" which is exactly what they are.


Heat and work are scalar quantity, but in thermodynamic given a system work and heat can flow through it. For the second this must be obvious to all: heat flows, i.e. a system can lose/acquire heat to/from the sorrounding. For work, you must take into account that a system also can do work into the sorrounding and viceversa. There are some conventions: heat assorbed by a system take positive values while heat flowing out of a system take negative value. The converse happen to work, if a system do some work to the surrounding its value is positive, negative in the other case.


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