# Why mole and kelvin are basic units?

1. Dec 3, 2012

### jd12345

Mole is just a number. It doesn't really measure anything so why is it a fundamental unit?
And with kelvin - it represents the average energy of the atoms/molecules in a compound. Why is it a fundamental unit? Temperature can easily be represented in joules.

2. Dec 3, 2012

### Staff: Mentor

So,moe of the mole usage, history units of measure controversy is described in the wikipedia article:

http://en.wikipedia.org/wiki/Mole_(unit [Broken])

Last edited by a moderator: May 6, 2017
3. Dec 3, 2012

### jd12345

I have basically the same point as the wikipedia article states. So why is it still called a fundamental unit?
Also for kelvin - why is it a fundamental unit as it represents energy

4. Dec 3, 2012

### the_emi_guy

As you said, it is just a word that represents a count, much like the word "dozen" or "gross". Do you understand why we need such as number in chemistry? In the chemistry lab you are measuring out quantities in grams, but you need to keep track of how many elementary entities you have, not in absolute terms but relative to other substance that you are also measuring in grams. Have you studied stoichiometry problems yet?

The kelvin temperature scale is unique in that 0 degrees represents the lowest possible temperature, where all thermal motion ceases.

5. Dec 3, 2012

### jd12345

Well I do understand why we need mole. But why is it a fundamental unit.?
You can just define mole to be 6.022 * 10^23 and use the word.

6. Dec 3, 2012

### f95toli

Fundamental units are called "fundamental" because there is no practical way to express them in terms of other units.
The fundamental units in the SI are there because 1) They are usedful and 2) They can be realized, i.e. it is something that can be measured and used to calibrate instruments.

It is important to understand that the SI is a practical system of units, ultimately it is is system designed in such a way that we can calibrate instruments in a self-consistent way.

This is why the mole and the Kelvin are there, there is no way to express in in terms of other fundamental units in a way that can be used for calibration/comparissons; and both the mole and the Kelvin are (obviously) very important units so they have to be fundamental.

7. Dec 3, 2012

### jd12345

Oh I had the wrong idea of what a fundamental unit is. I thought it should represent something physical which we can measure.
Okay now mole and kelvin makes sense. Thank You!

8. Dec 3, 2012

### Staff: Mentor

In fact, there is a proposal to do exactly this (with a slightly different constant), which may be considered for adoption by the "authorities" in 2014:

http://en.wikipedia.org/wiki/New_SI_definitions#Mole

9. Dec 3, 2012

### D H

Staff Emeritus
No, it can't. For one thing, temperature is an intensive property while energy is an extensive property. Temperature in some simple cases can be represented as energy per mole, perhaps, but not energy.

Even in those simple cases (i.e., ideal gases), using energy/mole in lieu of temperature doesn't quite cut it. Consider a vessel that contains two gases separated by an impermeable wall that transmits heat. Put some quantity of an ideal gas in one half, some quantity of another ideal gas in the other half. Heat will be transferred across the wall from one gas to the other if the two gases are at different temperatures. Heat may or may not be transferred if the two gases have different specific energies. For example, one gas is monatomic, the other diatomic.

Real gases aren't ideal, making the relationship between temperature and specific energy a non-linear one. Things get even worse when you consider the fact that gases can condense, liquids can freeze, chemicals can combine. The concept of temperature is very useful and is measurable. Specific energy is less useful, plus how do you measure it?

10. Dec 3, 2012

### Staff: Mentor

In statistical mechanics, we can define temperature via

$$\frac{1}{T} = {\left( \frac{\partial S}{\partial U} \right)}_{N,V}$$

where $S = k \ln \Omega$ ($\Omega$ being the multiplicity of the system).

If we wanted to be really fundamental about units, we would make entropy a fundamental quantity, and use the numerical value of k to define the unit of entropy which we might call the "boltzmann" (B).

Then the kelvin would be a derived unit: 1 K = 1 J/B.

11. Dec 3, 2012

### f95toli

kB will -unless I am misstaken- actually be defined in 2014. The general "philosophy" of the new SI (which is slowly being introduced) is to have one fundamental constant per unit and then realize the unit by e.g. counting (similar to what we do with the meter and the speed of light).
Hence, the Boltzmann, Avogadros constant, e etc will all eventually be defined to have definite values.

12. Dec 3, 2012

### _Abstraction_

A mole is just a number like "dozen", it's not a unit of measurement since it doesn't measure anything. A meter is a measurement of length, a second is a measurement of time, a gram is a measurement of mass, and a kelvin is a measurement of temperature, but a mole isn't a measurement of anything.

Last edited: Dec 3, 2012
13. Dec 3, 2012

### f95toli

It is a unit of measurement in the SI. This is if you want a political decision more than a a scientific one (but again, the reason is that is practical and useful to let it be a base unit).
Since Avogadro's constant is not a defined number you can't -at the moment- use that to realise the Mole. Hence, there are other methods for realising the mole, but neither of them directly involves counting anything.

14. Dec 3, 2012

### Khashishi

Basically, Boltzmann's constant is just a historical artifact. It should be regarded as a unit conversion factor between energy and temperature units. In plasma physics, and several other fields, temperature is measured in units of energy (typically electron volts), dispensing with Boltzmann's constant.

D H: Temperature and energy don't have to mean the same thing to use the same units.
jtbell: In statistical mechanics, (fundamental) entropy is unitless, being nothing more than the natural logarithm of a number of states. Temperature has the units of energy/entropy, which, therefore, is just the units of energy.

The equipartition theorem states that the average energy in an accessible degree of freedom is 1/2 the temperature times the Boltzmann's constant. If we get rid of the Boltzmann's constant, we can just give temperature in energy units, which is a lot more natural and simple.

Last edited: Dec 3, 2012
15. Dec 3, 2012

### ThinkerofWhat

A mole is the number of atoms that have a mass of 1 gram of hydrogen (single atoms, not H2). It is not arbitrary. Comparitively, the periodic table has on it the atomic mass of each element. You'll note that the atomic mass of hydrogen is not exactly 1 gram/mole, I think this is due to more accurate measurements, or the inclusion of isotopes. The atomic mass of each element on the periodic table is a per mole measurement, all relating to hydrogen's mass. As such, you can determine how much more massive each element is (per quantity) than hydrogen (per same quantity).

Since you can determine the quantity of molecules or atoms of a substance by it's molecular mass/mole, you can figure out how many grams of a substance to add to another substance to predict a chemical reaction.(because molecules combine in predictable quantities with other molecules)

The 'gram' measurement is related to the mass of one cubic centimetre of H20. A meter is the length of 100 cm, and is otherwise recorded somewhere as the number of wavelengths of a certain frequency of light, or the distance light travels in a certain time. I think that length is a truly arbitrary value (check an historical reference), and water is an arbitrarity chosen element (for historically obvious reasons).

Last edited: Dec 3, 2012
16. Dec 3, 2012

### DrDu

The problem with statistical entropy is that to use it as a fundamental quantity we would have to be able to count and identify all the relevant microstates. I don't see that we have even an idea to do so for a real system.

17. Dec 3, 2012

### jbriggs444

While this was the original definition, the current definition is the number of atoms in a mass of 12 grams of carbon-12.

http://en.wikipedia.org/wiki/Mole_(unit)

Last edited by a moderator: Dec 3, 2012
18. Dec 3, 2012

### the_emi_guy

Interesting idea, but is it practical? Let's say I am in a biology lab and I need to measure the temperature of a blood sample. To have the thermometer read out in units of energy, it would have to be calibrated to the specific heat of this particular blood sample.

19. Dec 3, 2012

### Khashishi

No specific knowledge of the specific heat of the sample is needed. The only difference is the unit of measurement. 1 K = 1.3806488*10^-23 J.
However, it isn't practical for everyday usage simply because of the huge difference in magnitude. Room temperature is on the order of 10^-20 joules.

Both Boltzmann's constant and Avogadro's number are used to connect the microscopic scale to human scale, and therefore have similar values. We could get rid of kB and just express temperatures in terms of J/mol, and the scales would be reasonable.

20. Dec 3, 2012

### the_emi_guy

Khashishi,

Forgive me, I am still unclear on this. I thought that heat capacity was the conversion from energy to temperature.

As you mentioned earlier, the constant of proportionality between E and T is 1/2(K) per degree of freedom.

For simple substances (monatomic gasses, perhaps plasmas) we know how many degrees of freedom are involved so we can convert freely between E and T.

But how many degrees of freedom should we assign to a blood sample?