On the subject of yesterday’s lesson, power, I thought I would briefly talk about one of the world’s most extravagant demonstrations of electrical power, the Z-Machine at Sandia National Laboratories. For those who have never heard of it, the Z-Machine is basically a very large energy storage device and it is used to produce extremely hot plasma, focused onto a very tiny area, in an attempt to create a nuclear fusion reaction. This machine is capable of firing pulses of energy close to 290 terawatts. That’s 290,000,000,000,000 watts! That's 80 times the world's electrical power! But you may be asking yourself, how this is possible?
The answer comes down to the unit time in which the energy is discharged, and that time is equal to about 100 nano seconds. To give you an idea of how short of a time frame that is, 100 seconds is to 100 nano seconds as the diameter of the earth is to the width of a human hair.
The interesting thing about this is how much energy is actually consumed during this event.
If you remember from yesterday’s lesson, power is equal to a change in energy per change in time (dw/dt). Sparing everyone the mess of a derivation of the equation, the expended energy can be written as..
w = the work done in joules
p = the power in watts
Δt = the change in time
Now we have an expression for the energy consumed within a time frame, where Δt is the change in time. Now you simply fill in the blanks! Remember that the Z-Machine fires a 290,000,000,000,000 watt pulse in 100 nano seconds.
We get about 29 mega joules. It may not seem like it, but that's actually not very much energy considering the power discharged.
Well that was longer than intended. Hope you found that real world application interesting! Lesson two will be posted later this week.