# Fun with E = mc2

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```					Fun with
E = mc 2

Samir Dhurde
IUCAA, Pune
E = mc2 is everywhere!
Does this mean that…
   Equations don’t scare us?
   We can use science just like scientists?

   We don’t need to go to school !?
   We can get all Science off Discovery Channel?
   Everyone knows what Einstein knew?
OR  
   Science is bad because people can make
bombs out of it?
What do you think of…
Energy (in joules)
= Mass (in kilograms) X
The Speed of Light Squared
(in meters squared per second squared) ?
Complex Science?!?
Its our same old friend E = mc2
But did you know these units?
No…
Because you never used E = mc2 !!!
for us…
Knowing = Memorising
≠ Using
So lets use it…

How much energy will one litre of
water yield if it is converted entirely
into Energy?
Isn’t that a strange question?
Neither can goes
of it’s Not!
Lots No energy be
E = mc2 tells you
into making even a
destroyed but, under
exactly how much
Matter and Energy are
small mass and it can
special circumstances,
forms a given
twoenergyof the same
also can be turned
eitherbe got back in
amount of mass
into thing!
some form.
the other
contains.

Use it Properly!
The speed of light…
   Light travels three hundred million meters in
a second i.e. 300,000,000 m/s
   A meter is as big as a ???
That’s a
   So (forgetting the units for now)                     BIG
lot
Energy = mass x (300,000,000)2
or     E = m (90,000,000,000,000,000)
= m (9 x 1016)
(this form is easier to use isn’t it?) .
Mass
   What is the mass of 1 litre of water?
   A litre of water is defined to have a mass of
one kilogram!
m=1


 So, E = 1 (9 X 1016)
= 9 X 1016 Joules
That is it!
Was that tough?
You just fruitfully used Einstein’s Equation!!!
What else can you find out about?

What could all this
energy
be used to power?
Energy & Power
   A Joule is the effort required to push one
kilogram over a meter at an acceleration of
one meter/second2.
   A Joule expended continuously for one
second is a Watt.
   A litre of water, converted to energy
could power a 1 watt light bulb for…
9x1016 seconds, or 2.5x1013 hours
or ~3 billion years! (2/3 the age of the Earth)
A 100 Watt bulb…
   would only stay lighted for 2.5 x 1011 hours!
There are about 109 families on Earth
   So let’s light 109 bulbs of 100 Watt power
for 250 hours…!

You
spend the same amount of energy
as a 100 watt bulb !
[Hint: One joule is equal to about four food calories]

200,000 people have been killed by just 2 atomic bombs.
One Hydrogen Bomb could kill 50 times as many!
Best use…

   All our energy
comes from the
Sun!
   The Sun has
E=mc2 as its
source of energy.
Nuclear Fusion
   When 4 hydrogen
nuclei are fused
together into 1 helium
nucleus, energy is
released in the form of
Light photons and
particles called
neutrinos.
But where does the mass come from?
   Mass of 4 hydrogen nuclei is more than
that of 1 helium nucleus

   So after fusion a little bit of mass is left
over. This mass deficit appears as the
energy of light and neutrinos.
A look inside…

The  fusion happens 700,000 km deep in the Sun’s core.
It needs unbelievable temperatures of 15 million degrees.
More E = mc2
The Sun emits 4 x 1026 joules per second

   How much mass does it
convert each second in
order to shine?
   If the Lifetime of the Sun
is 1010 years, how much
mass would it need in that
time?

Use m = E/c2 !
What Einstein didn’t tell us…
How do you convert any mass to Energy?

   Scientists are trying to make a sun on the
Earth. A fusion reactor that uses hydrogen.
   Hydrogen is the simplest & lightest element.
   Hydrogen is abundantly found in water!
   Hydrogen fusion has been tried and tested in
Nature and on Earth (in H-Bombs).
Keep trying Doc…
Why haven’t we done it?
   Hydrogen is a diffuse gas and it is difficult
to get its nuclei close enough to fuse.
   They start colliding into each other only at a
temperature of 15 million degrees C.
   We need to keep it both hot & dense.

We would use up a lot of energy to start it
and to keep it from exploding!
Use what you have properly…
Solar Lighting
Solar Heater
Solar Cookers
Science is not storytelling…
…its also painstaking observations of Nature.

“Respect Nature”

Thank You

```
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