The discussion revolves around the nature of temperature and whether it can be considered a vector quantity. Participants explore the implications of temperature as a scalar versus a vector, discussing its representation in different contexts such as potential fields and quantum systems.
Participants express multiple competing views regarding the classification of temperature as a vector. There is no consensus on whether temperature can be treated as a vector quantity, with some arguing for its scalar nature while others suggest contexts where it may exhibit vector-like properties.
The discussion touches on various definitions and interpretations of vectors and scalars, as well as the implications of temperature in different physical contexts, such as quantum mechanics and thermodynamics. The limitations of these definitions and their applicability to temperature are acknowledged but not resolved.
I like Serena said:The operations are well defined mathematically.
Left on their own they may make no physical sense, but as an intermediate step to a result, they do make sense.
So you add 2 temperature vectors. The result makes no physical sense.
Then you divide it by 2.
There! You have the average of the temperatures, which does make physical sense.
Same thing for calculating a variance, where you would add the additive inverse of the vector to the vector with the mean temperatures.
Next you would multiply the vector with itself to find the vector with squared errors.
DaleSpam said:More importantly, for every element of a vector space there is an additive inverse which is also an element of the vector space. In most systems a temperature of 300 K makes sense, but a temperature of -300 K does not. So for most systems temperatures wouldn't be elements of a vector space.
I am also not certain that addition of temperature makes sense physically. I mean, if you add a system of 300 K to a system of 400 K you don't usually get a system of 700 K. Contrast this to momentum where if you add a system of 300 kg m/s to a system of 400 kg m/s you do get a system of 700 kg m/s.
Hootenanny said:No it doesn't! You are standing in the same spot. Just because you are looking in a different direction doesn't mean that the temperature will be different.
The temperature only depends on where you are, which is why it is a scalar [field] and not a vector!
Try it: Take a thermometer and stand in your house/school/gym/park facing east (or any other direction you choose). Then, turn by 90 degrees. Does the temperature change?
That still wouldn't change anything. The temperature only depends on your position, not your orientation. It doesn't matter whether your environment is in equilibrium or not. Provided your thermometer is in the same position, it will register the same temperature regardless of its orientation.nouveau_riche said:as i said what you might call as temperature is the equilibrium state,where energy is distributed,do the same experiment as u suggest but with a condition that in that room there is a heater which is just being switched on
KE is not a vector either.nouveau_riche said:depends upon the K.E distribution of particles around
Hootenanny said:That still wouldn't change anything. The temperature only depends on your position, not your orientation. It doesn't matter whether your environment is in equilibrium or not. Provided your thermometer is in the same position, it will register the same temperature regardless of its orientation.
DaleSpam said:KE is not a vector either.
Please see the above discussion, temperature does not form a vector space.
Are you even reading what I have written? This is precisely my point. The temperature doesn't depend on orientation only position. That is why the temperature is a scalar field, rather than a vector field.nouveau_riche said:why it wouldn't,when i am near the heater the thermometer will give a higher reading than at the other end
that is not my orientation,that is my position
Because it is defined as a scalar.nouveau_riche said:why not?
HallsofIvy said:Since we are talking about vectors in space, the crucial point is how they convert to a different coordinate system. If your "vector" has temperatures at different locations as components, how do they change if you rotate the coordinate system?
Halls was asking about the temperature itself.nouveau_riche said:rotating a coordinate system will change the position vector(of the point,which i am measuring) given by vector laws
Hootenanny said:Halls was asking about the temperature itself.
Hootenanny said:Are you even reading what I have written? This is precisely my point. The temperature doesn't depend on orientation only position. That is why the temperature is a scalar field, rather than a vector field.
In a manner of speaking, yes. In a vector field, each point is associated with a value and a direction. However, in a scalar field, each point is only associated with a value.nouveau_riche said:so a vector takes into account the orientation?
See above. This has all been covered in detail.nouveau_riche said:why not?