After looking at several definitions,Vectors are quantities having both magnitude and direction.Heat has a magnitude and also a specific direction(from higher temperature to lower temperature)...so why is it considered as a scalar but not as a vector?
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5 Answers
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Heat, by definition, does not have a direction. It is just the amount of energy transferred some thermal process. The quantity you're asking about is the heat flux, which is a vector. (Note that heat does not have to travel from higher to lower temperature; it can and does go the opposite way!)
Similarly, energy does not have a direction. If you have an electromagnetic wave traveling in some direction, it carries energy with it. That energy still doesn't have a direction. Instead, there's a new quantity, the Poynting vector, that is a vector and describes the direction of energy transfer. That is the way it is with heat. Even when heat is moving, we don't say the heat has a direction. Instead we define a new quantity for that.
answered May 6, 2018 at 16:56
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$\begingroup$ thanks!you cleared it up for me....our physics teacher was telling something about heat only having a single direction or whatever...but now its all good...thanks again! $\endgroup$ Commented May 6, 2018 at 17:05
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1$\begingroup$ @user7657046 - Heat only spontaneously - that is, without any external active agent - flows from the hotter body to the colder one (and so no flow at equilibrium, i.e. when they are at the same temperature). But if there is an active agent doing work on the system like a heat pump, you can indeed make heat go the other way, and this is how a refrigerator manages to produce a cool spot in an otherwise uniformly-warm room. $\endgroup$ Commented May 7, 2018 at 11:35
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$\begingroup$ Heat always travels from higher to lower temperature, even in refrigeration systems. $\endgroup$ Commented Jul 6, 2020 at 16:21
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$\begingroup$ @David, Suppose we have a refrigerator at 10C in a room at 20C. We use refrigeration to cool the refrigerator down further, from 10C to 5C. To do this, we move heat from inside the refrigerator to outside it. So heat moves from colder to hotter. $\endgroup$ Commented Jul 6, 2020 at 16:26
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$\begingroup$ No ... heat does NOT move from colder to hotter. Low pressure and low temperature refrigerant is colder than the inside of the refrigerator, so it absorbs heat. The compressor does work on the refrigerant to raise its pressure and condensation temperature above room temperature, where the heat is expelled into the room, and this process is also transferring heat from hotter to colder temperatures. $\endgroup$ Commented Jul 6, 2020 at 16:33
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A vector quantity isnt something that just has magnitude and direction.One more necessary condition is that it should follow law of vector addition.Example-Current .It has both direction and magnitude but is not vector.
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$\begingroup$ This new question might be of interest to you: physics.stackexchange.com/questions/404453/… where your example of current not being a vector because it doesn't follow the vector addition law is challenged by applying it on current density. $\endgroup$– SteevenCommented May 7, 2018 at 11:02
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To add to the other already good and simple answers, let me add the following analogy.
Think of heat $Q$ as you would think of e.g. speed $v$ or distance $s$.
- Speed is considered a scalar without direction, because it is the magnitude of velocity $\vec v$, which does have direction.
- Distance is similarly considered a scalar without direction, because it is the magnitude of position $\vec s$ that does have direction.
- And keeping that thought, heat $Q$ can be though of as the "magnitude" of its vector counterpart - whichever that might be - which would define a related direction.
Such a heat vector counterpart is not something I have ever seen defined. So it might simply not ever have become useful enough for anyone to "invent", define and name. As heat (as an energy amount that is being transferred) is already a kind of "fluffy" and not very tangible term, its directionality is not an easy concept to think of.
Not even the closely related term heat (flow) rate, being an energy-per-second measure, is defined with direction. Only when reaching a term like heat flux (as pointed out in another answer), being an energy-per-second-per-area measure, do we start caring about the direction and thus define it as a vector. Only here does directionality start to become relevant and useful.
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Heat flows from one body to another. Consider 2 persons A and B. A has 10kg(of some stuff) in his hand and B has 20kg in his hand. If A gives 2kg of this stuff to B, I state "2kg has flowed from A to B." But mass is not a vector. Q amount of this quantity flows decreasing its value at the source by Q and increasing its value at the receiver by Q. It is all about the definition and the laws that govern the quantity. You may even succeed in defining a vector quantity closely related to heat. As Mark says, heat flux is the vector you are looking for.
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$\begingroup$ thank you for spending your time to reply to my question...i finally get the concept $\endgroup$ Commented May 6, 2018 at 17:07
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1$\begingroup$ Not only that "heat" as such has no direction, it is not even a quantity that can be measured in a body or even assigned to a body in any meaningful sense. "Heat" does not flow anywhere, instead energy flows and entropy flows when one speaks of "heat flow". $\endgroup$ Commented May 6, 2018 at 19:11
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Heat is a scalar quantity because it is not obey vector addition laws.
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$\begingroup$ @Sam I strongly disagree with your comment. Maybe incomplete, but that is the answer, I could just notice that it duplicates previous answer by Panda. $\endgroup$ Commented Jul 6, 2020 at 18:49