# Why is heat a scalar quantity?

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?

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.

• 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! – user7657046 May 6 '18 at 17:05
• @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. – The_Sympathizer May 7 '18 at 11:35

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.

• 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. – Steeven May 7 '18 at 11:02

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.

• thank you for spending your time to reply to my question...i finally get the concept – user7657046 May 6 '18 at 17:07
• 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". – hyportnex May 6 '18 at 19:11

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.