# Brought to you by the ketter K

Hey, sorry for having no Sunday Function yesterday. Life and travel conspired in such a way as to prevent it. Well, there’s always next week! But hey, at we have a post for today.

In physics, as in all mathematical disciplines, we have a lot of need for equations. Those equations contain letters which represent various numbers or quantities. We have plenty to choose from, with the letters both Latin-derived and Greek-derived. Even so that’s only a couple dozen letters, and there’s a lot of things to represent. E might be energy, or electric field. C might be the speed of light, or just a generic integration constant. But I bet the worst offender if terms of being used for different things is the nondescript and unassuming letter k. Offhand:

k – the spring constant in Hooke’s Law.
kbBoltzmann’s constant
k – the Coulomb force constant, k = 1/(4 π ε0)
k – another name for the z direction
k – (with a hat over it), the unit vector in the z direction
K – Kelvin degrees
K – the metric prefix for kilo
k – the wave vector
k – the wavenumber (the magnitude of the above wave vector)
k – a generic (usually integer) constant, after m, n, and l are already used.
k – a Latin index running over 1,2, and 3 for tensor notation in electrodynamics, general relativity and other fields.
K – kinetic energy
KJ – the Josephson constant
K – one of several variants of K mesons in particle physics

Are the more? Almost certainly, this is just what I can remember in 5 minutes of thinking. Maybe it’s time for some new letters.

1. #1 Blaise Pascal
October 27, 2008

A couple of corrections:

Kelvin isn’t measured in degrees, so saying K stands for Kelvin degrees in incorrect. It’s just Kelvin (or possibly Kelvins).

The SI prefix for 1000 is not K, but k.

2. #2 andy b
October 27, 2008

I have been outposted by a speedier pedant. I was leaping to the keyboard over the k = 10^3 issue…

October 27, 2008

k is often used for thermal conductivity as well.

4. #4 Zifnab
October 27, 2008

And strikeouts in baseball. Not sure if that counts.

5. #5 Alex M
October 27, 2008

Also, k is used for the dielectric constant!

6. #6 C. Chu
October 27, 2008

There are 26 Roman letters and 24 Greek letters, giving us a total of 50, not to mention we have two cases for 100 different letters. I’ve always wondered why we don’t use more of them.

7. #7 mph
October 27, 2008

In observational astronomy, K is the photometric correction for an object’s redshift (your filter passband corresponds to a different part of the object’s rest-frame spectrum, depending on its redshift).

8. #8 Chris P
October 27, 2008

Kt is a DC motor torque constant
Kv is a DC motor voltage constant

In the SI system these numbers are also THE SAME.

Rather cool and useful and a good slap around the head for those people who want to use imperial units.

9. #9 John-Michael Caldaro
October 27, 2008

There is a big sign in my high school physics classroom that says “We speak mks here!” I call it the alphabet of physics but it is really the alphabet of science, the SI system. As confusing as the letters for “quantities” is there are letters for the units of all these quantities. And some of the unit letters are the same as other quantity letters. The normal force is often represented by a capital N as a quantity and is measured in newtons, also a capital N. Another confusing one is the symbol for impulse, capital J. But this is the symbol for the unit of energy the Joule also a capital J. There are many others like this. I give quizzes at various times throughout the year aksing questions about quantities and units to see how much they have learned about the alphabet of Physics.

Scientists speak a language that takes a long time to learn. Each letter or group of letters has potentially very far reaching implications. Young students find this very daunting.

10. #10 Sarah
October 27, 2008

There’s a couple more uses of k in the analytical chemistry world that I’m presently blanking on, but will post when I have a chance to go through my class notes and find them.

11. #11 Eric Lund
October 27, 2008

There are 26 Roman letters and 24 Greek letters, giving us a total of 50, not to mention we have two cases for 100 different letters. I’ve always wondered why we don’t use more of them.

Not all of them are distinct. Capital Greek letters alpha, beta, epsilon, zeta, eta, iota, kappa, mu, nu, omicron, rho, tau, and chi are identical to capital Latin letters A, B, E, Z, H, I, K, M, N, O, P, T, and X, respectively. Lower case Greek letter omicron is identical to lower case Latin letter O (which is why TeX does not have a command for producing omicron). Also there is no way of reliably distinguishing a handwritten letter O (either case) from number 0; thus capital O is used only to denote order and lower case O is not used at all.

That leaves 85 characters. I wouldn’t swear that I have seen somebody use a capital xi, but I have seen all of the others used one way or another. I have also seen the Hebrew letter aleph used (to note a transfinite number).

12. #12 natural cynic
October 27, 2008

KD is the dissociation constant for a ligand-receptor complex in boichem. [hormone-hormone receptor, neurotransmitter-receptor etc.]

13. #13 Anonymous
October 27, 2008

K = Kip

14. #14 Anonymous
October 27, 2008

I’ve got to get out Shigley, the god-textbook of mechanical engineering for this, but:

In determining the endurance limit (ie. fatigue strength) of a material or part, the equation goes:

Se = kakbkckdkekfSe

Of the ‘k’s:
a = Surface factor
b = Size factor
d = Temperature factor
e = Reliability factor
f = Miscellaneous factor (I shit you not).

K = Stress concentration factor for various loading conditions; it has various subscripts to tell them apart.
Kk = Fracture toughness (yes, that’s K sub k)

In 2003 the American Gear Manufacturers Association standards for gear design also used ‘K’ with various subscripts for:
Stress correction, inertia factor, stress cycle factor, load distribution factor, overload factor, reliability factor, size factor, service factor, temperatre factor, dynamic factor, and the lengthwise curvature factor.
I’m sure there are others.

15. #15 teawithbuzz
October 27, 2008

Wait, nobody has said K is for Potassium? And before you tell me that’s chemistry, not physics, I would argue that chemistry is physics, at a small scale.

16. #16 dr. pablito
October 27, 2008

Loads of atomic physicists use potassium.

17. #17 dr. pablito
October 27, 2008

And of course, the k shell — the innermost electron shell of atoms, whence k shell electron capture, k shell x-rays. And for wavenumbers, it’s an abbreviation for Kaysers, inverse wavelength. Not often used anymore, but sometimes. And it’s used in 9-j symbols as another angular momentum vector.

18. #18 Leukocyte
October 27, 2008

Ka, dissociation constant of an acid (also chem, I guess)
Kb, dissociation constant of a base
Keq, equilibirum constant

19. #19 erik Remkus
October 27, 2008

The reason why capital xi might not be used is that it could be mistaken for the identical to sign when hand-written.

20. #20 sangfroid
October 27, 2008

The ebullioscopic (Kb) and cryoscopic (Kf) constants used in calculating boiling point elevation and freezing point depression, respectively.

21. #21 Chris
October 27, 2008

I seem to remember k_(greek letters, starting from alpha) being used to refer to various spectral lines.

22. #22 Taxorgian
October 28, 2008

I figured someone would have already mentioned that k is also used generally as a rate constant, especially in first-order decay, i.e., d(WIDE)/dt = -kWIDE, where WIDE stands for Whatever Is Decaying Exponentially.

23. #23 Jeremy Mohn
October 28, 2008

In population biology, the letter “K” refers to the carrying capacity of a population.

24. #24 Bob Hawkins
October 28, 2008

I used capital xi in my dissertation, mostly for the heck of it. Nobody complained.

25. #25 Shawn Wilkinson
October 29, 2008

lol, this post reminds me of K-theory

But in all seriousness, some are just typical abbreviations for units. For the constants, it wouldn’t surprise me if the reasoning has to do with how ‘C’, when written fast, can morph into all sort of different funny looking shapes, whereas k just looks like…k

Now, it is always entertaining when solving a multi quantum well problem a textbook uses not only k’s but kappas. I call bs.

26. #26 andy.s
October 29, 2008

k is the 3rd quaternion (I think this is actually the origin of the use of k-hat as the symbol for the z-axis unit vector).