Comments on: Fill my mental scientific tables.

Question: Fill my mental scientific tables.

SBMike — Tue, 17 Jul 2007 15:11:54 -0800

Scientists out there, what are the best physical constants or material properties to have memorized for back-of-the-envelope calculations?

For you scientists or engineers out there that work in the physical sciences, what quantities do you have memorized? I'm not looking to use these quantities for detailed scientific work or I'd look them up on a table. Just for making sense of the physical world, determining if some event is possible or not, or making quick estimates, what do you find useful to know off the top of your head?

Acceleration due to gravity on earth (9.8 m/s^2) is an obvious example. Probably knowing the density of Aluminum (~2700 kg/m^3) or steel (~7700 kg/m^3) would be helpful as these materials make up a lot of stuff in our world. Speed of sound in air (~340 m/s), modulus of steel (~200 GPa), specific heat of water (~4.2 joule/g*ºC) would be other examples.

I'm mostly interested in common materials or situations that you would come across everyday, so I probably won't be doing any quantum mechanics calculations or anything complicated like that, so no need for Boltzmann's constant, et al. Basic data about, say, the earth (air pressure at sea level = ~14 psi, rotational speed = ~ 1000 mph @ equator, distance from the sun = ~146 million km) or the human body (typical weight = 60-85 kg, walking speed = ~4 mph, top speed = ~15 mph, heat output = ~90 W, etc.) would be good too.

What quantities do you have memorized? Any tips on memorizing them myself?

(My field of study is materials science and metals, so answers pertaining to these would be very good, but I'm mostly just interested in general information)

By: kingtaj

kingtaj — Tue, 17 Jul 2007 15:32:52 -0800

Freezing point is 32 degrees Fahrenheit and 0 degrees Celsius.

Sorry, couldn't resist. It is a very useful.

By: DevilsAdvocate

DevilsAdvocate — Tue, 17 Jul 2007 15:36:29 -0800

Well, the most useful ones are the ones that are so obvious you didn't even think of mentioning them: normal body temperature, freezing/boiling points of water, speed of light, length of a day/year on earth, etc. Here's some slightly less common ones:

Human body:
Genome = ~3*10⁹ base pairs
Adult human = ~10¹⁴ cells

Earth:
Diameter = ~8000 mi
Density = ~5.5 g/cm³

Sun:
Diameter = ~900000 mi = ~5 light-seconds (!)
Power output = ~10³⁰W
Surface temperature = ~5900K
Core temperature = ~10⁸K

Atomic mass of common elements:
H=~1
C=~12
N=~14
O=~16
F=~19
Na=~23
P=~31
S=~32
Cl=~35.5
K=~39
Ca=~40

By: gregvr

gregvr — Tue, 17 Jul 2007 15:40:49 -0800

speed of light: 3 x 10^8. That's about all I have memorized!

By: janell

janell — Tue, 17 Jul 2007 16:08:24 -0800

kT at room temp is ~25 meV is pretty handy to know

1 pint of water wighs ~1 lb

By: janell

janell — Tue, 17 Jul 2007 16:09:00 -0800

Oooh, ooh, also that -40 C = -40 F, and that 28C = 82 F.

By: fshgrl

fshgrl — Tue, 17 Jul 2007 16:19:07 -0800

Most useful thing is knowing the conversions from metric to imperial to whateverthehellyouamericanscallyoursystem.

By: janell

janell — Tue, 17 Jul 2007 16:33:40 -0800

A few length scales:

a C-C bond is ~1 A

a human hair (depending on the person) has a diameter of 50-100 microns

By: Uncle Jimmy

Uncle Jimmy — Tue, 17 Jul 2007 16:46:14 -0800

Concrete has a specific gravity of about 2.5.
Soil has a specific gravity of about 1.5.

These figures obviously vary widely, but will get you within an order of magnitude.

By: Arturus

Arturus — Tue, 17 Jul 2007 17:08:31 -0800

The number of seconds in a year is approximately pi times ten to the seventh, to within 0.5% accuracy.

The inertial constant of a rotating solid sphere is 2/5.

By: caek

caek — Tue, 17 Jul 2007 17:10:51 -0800

Mass of the Sun = 2 x 10^30kg
Typical atomic separation/size = 10^-10m = 0.1nm = 1 Angstrom
Typical nucleus size = 10^-15m = 1fm

Google "Fermi problems" for examples of how to use these facts and you should be able to come up with the most useful ones.

By: caek

caek — Tue, 17 Jul 2007 17:11:39 -0800

π is about 22/7.

By: edd

edd — Tue, 17 Jul 2007 17:40:11 -0800

Boltzmann's constant isn't a physical constant, so you're wise to ignore it.

I think Avogadro's Number is useful. Given the appropriate formulas to hand, I'd take the density of air over the speed of sound in air.

Otherwise, I struggle to think of much else that hasn't been mentioned.

By: anthill

anthill — Tue, 17 Jul 2007 17:45:25 -0800

Ideal Gas Constant?

By: TheOnlyCoolTim

TheOnlyCoolTim — Tue, 17 Jul 2007 19:29:09 -0800

Google Calculator, which you can even access via SMS text, can be very good for these types of calculations.

You can do things like:

e joules per 2 coulombs * avogadro's number coulombs per millisecond * pi fortnights in electron volts

if you want. It knows all sorts of constants, dimensional analysis, conversion factors, different bases...

By: alikins

alikins — Tue, 17 Jul 2007 19:44:26 -0800

1 liter ~= 60 cubic inches
water weighs about 8.3 pounds per gallon
gas weighs about 6 pounds per gallon

By: bystander

bystander — Tue, 17 Jul 2007 20:22:36 -0800

Since it sounds you are American, can I suggest learning metric values? Lots (most?) scientific literature won't have miles, furlongs, pecks and gallons. I see you have for some of the examples, so it might be useful to learn the metric equivalents of imperial measures you know.

By: jpdoane

jpdoane — Tue, 17 Jul 2007 20:26:20 -0800

"I'm mostly interested in common materials or situations that you would come across everyday, so I probably won't be doing any quantum mechanics calculations or anything complicated like that, so no need for Boltzmann's constant, et al."

If you really want a constant that almost all scientists and most engineers would use on a regular basis, your answer is pi = 3.14159...

Beyond that, it really depends on what you are doing. Most scientist/engineer types have pretty specific areas of focus, so the constants they use everyday wouldn't necessarily be the general science knowledge sort of things you mention (temp of freezing water, size of earth, etc), but rather those things that relate to the specific field they are in.

By: jpdoane

jpdoane — Tue, 17 Jul 2007 20:27:17 -0800

Oh, and e, but I admit I don't know it off the top of my head (darn you TI-85 and your wonderful bank of constants)

By: willconsult4food

willconsult4food — Tue, 17 Jul 2007 20:38:05 -0800

To paraphrase Arturus:

"Pi seconds is approximately equal to one nano-century."

By: flaterik

flaterik — Wed, 18 Jul 2007 02:33:28 -0800

Diameter = ~900000 mi = ~5 light-seconds (!)

I never really thought about the sun's size in terms of c, and it is currently boggling me.

That is one big ass ball of fire.

By: DevilsAdvocate

DevilsAdvocate — Wed, 18 Jul 2007 04:49:35 -0800

Boltzmann's constant * Avogadro's Number = Ideal gas constant
so pick any two of those and you can derive the third.

1 gallon = 231 in³ (exactly)

By: JJ86

JJ86 — Wed, 18 Jul 2007 05:55:30 -0800

Civil Engineer here. Mostly I need to remember formulae and unit conversions but here is one constant that comes in handy quite often:

Density of Water=62.4lb/CF

By: edd

edd — Wed, 18 Jul 2007 09:06:21 -0800

And now I'm wondering why I was critical of Boltzmann's Constant for not being a physical constant and then suggested Avogadro's Number which is essentially the same sort of thing - a unit conversion factor. Ah well.

By: The Esteemed Doctor Bunsen Honeydew

The Esteemed Doctor Bunsen Honeydew — Wed, 18 Jul 2007 15:42:56 -0800

A pint's a pound the world around

(granted that wherever you are in the world, they're using imperial measures, and also that your liquid is water-like (anything from olive oil to light syrups))

By: aimless

aimless — Wed, 18 Jul 2007 19:58:33 -0800

C1 * V1 = C2 * V2

where C1 is the concentration of a solution you have and C2 is the concentration you want to get to. V1 is the volume you have (or need) of solution at C1, and V2 is the volume you want for C2. Solve for V1 and add enough solvent to reach V2, and you have C2.

I haven't used this in real life, but I use it all the time for diluting solutions in the lab. it seems like it might come in handy someday if I wanted to dilute children's medicine or juice or something. Maybe you never need to get that specific in real life, though. Cooking maybe?