Is temperature considered a scalar quantity?

[Herman Trivilino]

I am trying to describe vector and scalar physical quantities, without defining vectors and scalars mathematically.

You need only one number to specify the value of a scalar. You need more than one number to specify the value of a vector.

Your notion of being able to add two numbers together to get something meaningful depends on what you're adding, not on whether something is a scalar.

 

[Chris Miller]

Seems like it'd be the result of averaging, and inseparable from volume. E.g., 1 cup of 100C water and 2 cups of 70C water = 3 cups of 80C water.

But this doesn't consider SR as, at super high temperatures, molecules approach the speed of light, if they even do/can? No clue.

 

[bob012345]

You should appeal to the student's common sense. Mix hot water with cold water. You don't get hotter or colder water; you get lukewarm water. Every student knows that. So based on that example, the students themselves can say that the temperatures don't add.

It is a good science lesson for students. Whenever your scientific calculation disagrees with what you experience in daily life, that is a clue that you're applying the science incorrectly. Teach them that and teach them that the wrong answer is to presume that the science is incorrect in such cases.

Also note what @Drakkith said about intensive versus extensive properties. That illustrates that vector versus scalar is true but it is insufficient to describe all the properties. Students should be able to see from ordinary life that intensive/extensive vector/scalar are not the same thing, and that they can exist independently.

Also, intuitively, mixing substances with different temperatures is like mixing paint with different colors. If both batches are blue, the mixture is blue regardless of the relative amounts. If one batch is yellow, the result is not blue or yellow but some shade of green weighted by the relative amounts of blue and yellow. Same is true for mixing different substances at different temperatures only the scalar which directly adds up is actually the thermal energy of each batch. Energy adds directly because it's conserved and thus the total energy before mixing is equal to the sum of each batches mass times it's specific heat capacity times it's temperature and the energy after mixing is also the sum of the product of each batches mass, heat capacity and temperature only now the temperatures are the same. It's an energy conservation problem.

 

[sophiecentaur]

Seems like it'd be the result of averaging, and inseparable from volume. E.g., 1 cup of 100C water and 2 cups of 70C water = 3 cups of 80C water.

Endless lessons with "The Method of Mixtures" at O and A level showed me a lot about experimenting. No negatives involved in our lab though.

 

[Rap]

As Terry Bing said, you can add and subtract temperatures, but the question is what does it mean? Sure, you can say that if you raise the temperature of an object by 2° and then by 3° it will be 5° warmer than it was. But the difference of temperatures has a real physical meaning beyond even that. Heat engines operate between two bodies whose temperature difference determines the power and the efficiency of the engine. Also, the rate of transfer of energy from a hot body to a cold body is proportional to their temperature difference, by Fourier’s law.

If you define a scalar as a one-dimensional vector then sure, you can add and subtract, multiply, divide temperatures at will and temperature is a scalar. If you define a scalar as a one-dimensional vector with physical meaning, then it gets iffy. Like what is the meaning of negative temperature?

 

[sophiecentaur]

If you define a scalar as a one-dimensional vector

I think that puts it well and points out why we don't actually define a scalar that way. There are a whole list of types of number and this discussion has shown why this is necessary because it has attempted and failed to classify numbers too crudely.