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?
        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

                    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
    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?) .
   What is the mass of 1 litre of water?
       A litre of water is defined to have a mass of
        one kilogram!

 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?
         Free your Mind!

           What could all this
           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…!

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

    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
   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
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

       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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