Question

Is the unit of Kelvin the same as Joules/mole?

Answer 1

No. Kelvin is a unit of temperature.

Answer 2

But isn't temperature average kinetic energy? So then it would make sense to me to say that the sum of all the individual kinetic energies of the particles divided by the total number, moles, is Joules/mole is it not?

Answer 3

http://physics.stackexchange.com/a/1677/567

Answer 4

Maybe you are confusing temperature (Kelvin) with heat (Joules).

Answer 5

PV=nRT

Answer 6

R is in J/(mol.L)

Answer 7

per kelvin

Answer 8

so!they are not the same!

Answer 9

Yes and no. Numerically they are distinct, but dimensionally they are not. That is, both kelvins and joules have the dimension of energy, for exactly the reason you give. The conversion factor is Boltzmann's constant (1.38 x 10^-23 J/K). The reason for the weirdness is because both the joule and the kelvin were defined before anyone realized they measured the same thing. It's not unlike the fact that we have complicated conversions between degrees Fahrenheit and kelvins.

Answer 10

Kelvin is the unit of temperature...Mole is the unit of atoms and molecules.......Joule is the unit of energy..

Answer 11

@Kainui

Answer 12

I originally came to this because of pV=nRT. It seemed like R was more of an artifact not a physical constant. You could just arbitrarily count temperature with R included instead of being based on 1/100th of the distance between 0 and 100 degrees Celsius.

This would put the "physical constant" at 1, and then it really comes down to being a way to "cheat" dimensional analysis so that everything works out all nice and tidy, which seems to be garbage unless you set Kelvin = Joules/mole which actually makes more sense to me.

Answer 13

:)...

Answer 14

no, it is degrees kelvin.

Answer 15

One of the problems you may be having is that the definition of temperature is a little tricky. It's a thermodynamic quantity, not a mechanical quantity, so it does not actually have a definition in terms of forces and masses and displacements, the way many other units do. It is formally defined this way:
\[\left(\frac{\partial S}{\partial U}\right)_{V,N} = \frac{1}{T}\]
The thing on the left is the partial derivative of entropy with respect to energy, holding volume V and mole number N constant. Physically speaking, to find the temperature of a system, you find out how much the entropy increases when you add an extra joule of energy. That quantity is the inverse of the temperature. If the entropy increases a lot, i.e. 1/T is big, then the temperature T is low. If the entropy increases only a little, i.e. 1/T is small, then the temperature T is big.

Hopefully this makes sense. It is particularly helpful to think about entropy as the number of states accessible to the system -- all the ways its particles could be arranged, in different locations and with different velocities. Consider a system that is frozen into a crystal: all the atoms located very close to lattice positions, moving very slowly, so that there are very few different states the system ever is in. This is a system with very low entropy. However, if you add even a little energy to the system -- i.e. speed up the particles -- then the number of possible arrangements grows rapidly. The particles can move further, and perhaps even the crystal melts, so that the particles can travel great distances and mix together. Since S grows rapidly with adding U, this means 1/T is big, which means T is low -- and indeed, this is a perfect description of a system at very low temperature.

But there's a diminishing rate of returns business here. As you keep adding more and more energy, the system eventually stops finding new states it can occupy. It boils, and then it can find all the states with its particles in any position in the container. Heat it some more and...well, not much happens, except the average speed goes up. Furthermore, the relative increase in speed for a given amount of energy gets smaller and smaller. So when you've added a lot of energy to a system, S changes only slowly with additional U, which means 1/T is small -- and T is big.

WIth this defintion in mind, you can address the issue of dimension of temperature. Entropy is dimensionless, since it's just the log of the number of states accessible to the system. That means dS/dU has dimensions of 1/energy, which means T has dimensions of energy.