My solar panels have generated 1500 kWh of energy since they were installed 6 months ago.
Now, Einstein tells us that energy has mass. How heavy is 1500 kWh? We can use E = mc2 to find out.
Here, E is 1500 kWh, the speed of light c is 186000 miles/second. Unfortunately, we can’t just divide 1500 by the square of 186000. Sure, that would give the mass, but not in any unit I’m familiar with – when you tell me how much something weighs, I want to hear it in pounds, or kilograms, or ounces… even centiweight would do, if I have Google handy.
Instead, dividing 1500 by 186000 squared would give the mass in “kilowatt-hours times squared seconds per square mile”. Useless.
Scientists use a standard system of units, where Energy is measured in ‘Joules’ (a Joule is a watt-second) mass is in kilograms, and speeds are in metres per second. Let’s use that system.
So, we need some conversions.
- There are 3600 seconds per hour.
- There are 1000 watts per kilowatt
So, I can multiply 1500 kilowatt-hours by 3600 seconds/hour, to make the ‘hours’ cancel out. I’ll get the energy from my solar panels in kilowatt-seconds – 5400000 kilowatt-seconds, in fact.
Likewise, there are 1000 watts per kilowatt. If I multiply 5400000 kilowatt-seconds by 1000, to cancel out the kilowatts, I’ll have the number of watt-seconds, or Joules, my solar panels have produced. Five point four billion.
To use Einstein’s formula, we also need to convert the speed of light to metres per second.
- There are 1.61 kilometers per mile, and
- There are 1000 metres per kilometer
So, the speed of light is 186000 x 1.61 x 1000 metres per second. About three hundred million metres per second (I could have just looked that up, actually). It’s fast. It’s a big number. Divide my 5.4 billion Joules by the square of 300 million, and you get a tiny tiny number of kilograms.
Nobody said energy was heavy.
Perhaps the answer would be more useful in, say, micrograms? There are a billion micrograms per kilogram.
Let’s do the whole calculation now:
E = (1500 kW.hr x 3600 s/hr x 1000 W/kW)
= 5400000000 W.s (you can think of the kW and the hr as cancelling out)
c = (186000 mi/s x 1.61 km/mi * 1000 m/km) = 300000000 m/s (again, the mi and km cancel out)
m = E / c^2 = (5400000000 W.s) / (300000000 m/s)^2 x 1000000000 mcg/kg,
which, if you remember that a Watt-second is a Joule, and that using Joules and m/s in Einstein’s formula gives the mass as kilograms, gives 60 micrograms.
My solar panels have generated 60 micrograms of energy since they were installed. My energy company charges me about six billion dollars per kilogram, making energy one of the most expensive things I buy.
After working this out, I got to wondering – how much saffron rice could I make, if this entire 1500kWh was converted into saffron?
Now, 60 micrograms of saffron isn’t much. But you don’t need much saffron.
I looked up various websites to get some conversions.
- From this online database, I learned that 1 US teaspoon contains about 708000 micrograms of saffron.
- This recipe tells me to use 1/8 of a teaspoon of saffron powder and 1 cup of rice. I suppose that’s 8 cups of rice per teaspoon of saffron. I haven’t tried the recipe. Do let me know if it’s good, before I waste 8 cups of rice.
- Lots of people have asked how many grains of rice in a cup, and get different answers. This website suggests there are 6000.
Now, I’m ready to work out how much saffron rice I can make with my 60 micrograms of solar energy.
- To convert 60 micrograms into teaspoons of saffron, I divide 60 mcg by (708000 mcg / tsp), so that the micrograms cancel out. I get 0.0000847 teaspoons.
- You need 1/8 teaspoons of saffron for a cup of rice – that’s 0.125 tsp / cup. I divide my 0.0000847 tsp by (0.125 tsp/cup) so the tsp’s get canceled out, and I get 0.000678 cups of rice.
- Finally, there are 6000 grains of rice per cup. Multiplying 6000 grains/cup by 0.000678 cups, and the cups cancel out. I’m left with 4.076 grains of rice.
So, if all the energy from my solar panels had been used to create saffron in some calvin-and-hobbesy duplicator machine, I’d have enough saffron to make about 4 grains of saffron rice.
Thank about that, next lunchtime!