Why isn't temperature a vector quantity?

[nouveau_riche]

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.

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.

the key idea in that temperature does not follow an addition of 300k + 400k=700k is the fact that temperature is seen as averages,when you say 300k ,this is the state of equilibrium,in that context the energy has been distributed uniformly giving it a scalar touch
and that is what @i like serena is trying to highlight
i suppose

 

[nouveau_riche]

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?

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

 

[Hootenanny]

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

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.

 

[Dale]

depends upon the K.E distribution of particles around

KE is not a vector either.

Please see the above discussion, temperature does not form a vector space.

 

[HallsofIvy]

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?

 

[nouveau_riche]

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.

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

 

[nouveau_riche]

KE is not a vector either.

Please see the above discussion, temperature does not form a vector space.

why not?

 

[Hootenanny]

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

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.

 

[Hootenanny]

Let me go back to basics and try to pre-empt a few questions and put an end to this thread once and for all.

why not?

Because it is defined as a scalar.

- Can you define it as a vector?
No.

-Why?
Because it won't make any sense, just as it makes no sense to call temperature a vector.

 

[nouveau_riche]

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?

rotating a coordinate system will change the position vector(of the point,which i am measuring) given by vector laws

 

[Hootenanny]

rotating a coordinate system will change the position vector(of the point,which i am measuring) given by vector laws

Halls was asking about the temperature itself.

 

[nouveau_riche]

Halls was asking about the temperature itself.

not in temperature

 

[nouveau_riche]

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.

so a vector takes into account the orientation?

 

[Hootenanny]

so a vector takes into account the orientation?

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.

 

[Dale]

why not?

See above. This has all been covered in detail.