Getting to know the Joule (J), an energy unit

The idea: Developing a familiarity with the Joule will help ground your further work with energy. Many sites provide definitions of joules for you, and many others describe equations in which energy is a variable. What I've never seen, on the web or in print, is a focused effort to help you become familiar with the size of the unit. No surprise then, that even many MIT engineering graduates, lack even an order of magnitude feel for the size of joules.

2003-Nov-30 -- I just now stumbled on this forgotten year+ old draft webpage. It seems worth finishing and placing online. But since the former is unlikely to happen any time soon, perhaps the latter will by itself serve. I don't recall how much care when into these draft numbers, so...
I suggest doubting these numbers unless/until you check them yourself.
Regardless, the objective of the page was to illustrate an approach - "quantitative grounding".
I'd love to hear comments. -- Mitchell Charity

One Joule

You up 1 to 3 mm.     (That's "up" against the Earth's surface gravitational field.)
A liter of water (10 cm cube) up 10 cm. (1 kg) (a 2L soda bottle falling over)
A cc of water (1 cm cube) up 100 m.

A 200 nm cube of water converted entirely into energy. (10-20 m3)
A couple of hundred viruses converted entirely into energy.

The kinetic energy of a crawling baby.
Of you slowly swaying.
Of a clapping hand.
A cell at 1% c.
A continental plate drift-ing.
1 kg at 1.5 m/s.
2 kg at 1 m/s. (slowly pushing a 2L soda bottle)

One second of sunlight on a 10 cm square patch of ground.

A rubber band or small spring.

CO2 pressure in a 1/4 empty 2L soda bottle.




Also - Some definitions

Energy. Work. Quantity of heat. The potential to do work (often a potential field with something to ready to fall through it). The SI derived unit for energy, work, quantity of heat.

Also - Some slicing and dicing of units

In SI, you measures time in units of seconds (s), mass in kilograms (kg), length in meters (m), area in meters squared (m2), speed in meters per second (m·s-1), and so on.

You measure energy in kilogram, meters squared, per second squared.


m × m × kg / s / s

But we often/usually slice this up.
depending on what we are doing.

For instance, kinetic energy is defined as 1/2 m v2 (said "one half m v squared", or "one half times mass times velocity squared"). Now as for units, 1/2 doesn't use units (of course), mass has units of kilograms, and velocity/speed has units of meters per second (m·s-1).
So kinetic energy has units of
Which, rearranging, is
or just our old/new friend

This all might look less unfamiliar as
1/2 m v2
kg × (m / s)2
kg × (m / s) × (m / s)
kg × m / s × m / s
kg × m × m / s / s
m × m × kg / s / s

Some common ways of slicing this up are...

Joule(m2·kg·s-2)Energy. The potential to do work. Often a potential field with something to ready to fall through it.
force·distance(m·kg·s-2)·(m)A weight waiting to fall some distance.
Newton meters (N·m)
mass·accel·distance(kg)·(m·s-2)·(m)A mass, trying to accelerate, lifted for some distance, and thus ready to fall.
A mass in motion, reluctant to stop.
mass·c2(kg)·(m·s-1)2 Conversion between the mass and energy flavors of massergy.
W·s(m2·kg·s-3)·sWatt seconds: Some time's worth of power.
V·A(m2·kg·s-2·A-1)·(A)Volt Amps: Some electrons (a current), upstream in a voltage (electric potential difference).
Wb·A(m2·kg·s-2·A-1)·(A)Weber·Amp: Some electrons, upstream in the voltage created by some magnetic flux through the conductor.
Pa·m3(m-1·kg·s-2)·(m3)Pascal·volume: A hunk of some presure or stress.
Coulombs2/Farads: A capacitor, of some roominess (F), with charge (C) stuffed in against itself.


Notes - re One Joule

mgh     E (J) = m (kg) × g (m·s-2) × h (m)     g = 9.8 m/s2 around the Earth's surface.
A mass m (kg) in a gravitational potential field with acceleration g (m·s-2, ie, "meters per second per second"), upstream a distance of h (m).

1 J
= ?? kg up Inf km.
= 4e-6 kg up 25 km. (typical raindrop - 1/2(2 mm)^3 = 4 mm^3 => 4 (1e-6) kg) [too high]
= 1e-3 kg up 100 m. (cc)
= 0.1 kg up 1 m. (1 m)
= 1 kg up 0.1 m. (1 kg)
= 2 kg up 50 mm. (2 liter bottle)
= 25 kg up 4 mm.
= 50 kg up 2 mm.
= 75 kg up 1.3 mm.
= 100 kg up 1 mm.
= 1e3 kg up 100 um. (m^3 water up hair's thickness)
= 1e9 kg up 1 A. ([1e9 kg is what in lead?])
[...other bodies]

mc2     E (J) = m (kg) × c2 (m2·s-2)     c = 3.00 × 108 m/s ; c2 = 8.99 × 1016 m2/s2

1 J = 10-17 kg converted to energy.
10-17 kg is
a hundred viruses or two
a 200 nm cube of water
1010 nucleons (1.7 × 10-27 kg each)
say 108 atoms

1/2 mv2     E (J) = 1/2 () × m (kg) × v2 (m2·s-2)

1 J =
1e-12 kg at 1e6 m/s. (cell at 1% c)
1e-6 kg at 1400 m/s. (mm^3 water at Mach 4+, eh)
1e-3 kg at 45 m/s. (cc gram)
.5 kg at 2 m/s. (clapping hand) [m_hand=0.00614*(50,100)kg=(.3,.6)kg]
1 kg at 1.4 m/s.
2 kg at 1 m/s. (slowly pushed 2L bottle)
10 kg at 0.45 m/s. (crawling baby)
50 kg at 0.20 m/s.
100 kg at 0.14 m/s.
1e22 kg at 1e-11 m/s. (plate drift) [a bit too slow, so a small plate]

10 cm square patch of sunlight, per second. (100-300 W/s surface) [10 cm is a bit too big]

Rubber band
src1, 2 : a small 8cm rubber band, or 3cm spring.

E = V F/A
1 m^3 at 1 Pa.
1/2 cm^3 at 2e6 Pa (290 psi, soda) src
1 cm^3 at e6 Pa (145 psi, 9.87 atmos)
1 dm^3 at e3 Pa (0.15 psi, 7.5 mmMg)

Mitchell N Charity <>

 Find and link to Benjamin's thesis re energy cluelessness.
 Continue work on the page.
 Describe philosophy, intent.  Quantitative grounding/familiarity.
 Is the 2L bottle CO_2 pressure total or partial?  If former, rephrase.

 2003-Nov-30  Online.  Added DRAFT warning, Notes/Doables/History.
 2002-Aug-05  Draft.