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?
[Physics] Why is heat a scalar quantity
temperaturethermodynamicsvectors
Related Solutions
To be precise, current is not a vector quantity. Although current has a specific direction and magnitude, it does not obey the law of vector addition. Let me show you.
Take a look at the above picture. According to Kirchhoff's current law, the sum of the currents entering the junction should be equal to sum of the currents leaving the junction (no charge accumulation and discharges). So, a current of 10 A leaves the junction.
Now take a look at the picture below.
Here, I have considered current to be a vector quantity. The resultant current is less than that obtained in the previous situation. This result gives us a few implications and I would like to go through some of them. This could take place due to charge accumulation at some parts of the conductor. This could also take place due to charge leakage. In our daily routine, we use materials that are approximately ideal and so these phenomena can be neglected. In this case, the difference in the situations is distinguishable and we cannot neglect it.
If you are not convinced, let me tell you more. In the above description (current as a vector), I have talked about the difference in magnitudes alone. The direction of the resultant current (as shown) is subtle. That's because in practical reality, we do not observe the current flowing along the direction shown above. You may argue that in the presence of the conductor, the electrons are restricted to move along the inside and hence it follows the available path. You may also argue that the electric field inside the conductor will impose a few restrictions. I appreciate the try but what if I remove the conductors? And I also incorporate particle accelerators that say shoot out proton beams thereby, neglecting the presence of an electric field in space.
Let me now consider two proton beams (currents), each carrying a current of 5 A as shown below. These beams are isolated and we shall not include any external influences.
Now that there is no restriction to the flow of protons, the protons meeting at the junction will exchange momentum and this will result in scattering (protons represented by small circles). You would have a situation where two beams give rise to several beams as shown below. Our vector addition law does not say this.
I have represented a few in the picture above. In reality, one will observe a chaotic motion. Representation of the beams (as shown right above) will become a very difficult task because the protons do not follow a fixed path. I have just shown you an unlikely, but a possible situation.
All this clearly tells us that current is not a vector quantity.
Another point I would like to mention is, current cannot be resolved into components unlike other vector quantities. Current flowing in a particular direction will always have an effect along the direction of flow alone over an infinite period of time (excluding external influences such as electric or magnetic fields).
Your definitions of scalars and vectors are fine.
In specific answer to your questions:
- and 3, are related, so I'll address them first:
$$\text{speed} = \frac{\text{distance}}{\text{time}}$$
and
$$\text{velocity} = \frac{\text{displacement}}{\text{time}}$$
Where distance is
a scalar quantity that refers to "how much ground an object has covered" during its motion.
displacement is
a vector quantity that refers to "how far out of place an object is"; it is the object's overall change in position.
$$\text{displacement} = \text{change in position} = \text{final position} - \text{initial position}$$
The direction is based on where the final position is with respect to the initial position.
(time is also a scalar)
(Reference for quotes about distance and displacement).
Due to velocity being calculated based on the vector displacement, velocity is also a vector (going in the same direction as the displacement). Similarly, acceleration is based on a change in velocity, so is a vector as velocity is a vector.
$$\text{acceleration} = \frac{\text{change in velocity}}{\text{time}}$$
in the direction of the velocity - if the acceleration is negative, the object is decelerating (slowing down) or accelerating in the opposite direction.
Similarly for question 2. Force is calculated using the vector acceleration:
$$\text{force} = \text{mass} \cdot \text{acceleration}$$
in the direction of the acceleration.
Best Answer
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.