I have been thinking about the fact that heat and work are the two manifestations of energy transition, not energy itself.
We all recall that Einstein codified the relationship between the rest mass of a substance and it’s energy by noting that energy is equal the mass of a material multiplied by the speed of light squared:
Sitting in front of me is a bottle of Scotch. It is not getting warmer or colder (which we recall from our discussion of specific heat means that heat is not being added to or taken away from it), nor is it doing any work. It’s just sitting there. And so, there is no change of energy of the scotch.
But there is energy in that scotch. Let’s see how much:
A very handy unit of energy is the Joule, defined as kilogram-meters-squared / seconds-squared
See why this is a great unit? It has meters-squared divided by seconds squared. Which is speed squared! A Joule is the work needed to push a force of one Newton by one meter. We recall that the units of a newton are kg * m / S^2, which is multiplied by a distance m.
Now, this bottle is about a quart in size, so in rough numbers saying it weighs about 1 kilogram (2.2 Lbm) is good enough for our purposes. And the 1 kg weight makes the calculation really easy.
The speed of light is 299,792,458 meters per second. That’s all we need to do our calculation:
1 kg * 299,792,458 m/s * 299,792,458 m/s = 89,875,517,873,681,800 Joules. That’s a lot of Joules!
There are about 1,055 joules in a Btu. Since we’ve been working with Btu’s previously we divide the Joules and come up with:
1 Bottle Scotch = 89,190,064,335,243 Btu.
We then recall that a gallon of gasoline contains about 114,000 Btu per gallon. So if we convert the energy represented by our scotch, we see that it is equivalent to 747,281,266 gallons of gasoline. Incredible!
Note, by the way, that this equation is indifferent to what the mass is made of. A pound of water holds the same amount of energy as a pound of scotch or a pound of feathers.
Now, a savvy reader is going to say, wait a minute, you can’t pour that scotch into a car and get the equivalent of three quarters of a billion gallons of gasoline worth of mileage. And that’s true. Because the energy (heat) liberated by burning gasoline is due to chemical bonds breaking and reforming, not the conversion of mass into energy, which is a nuclear, not chemical, reaction.
The point here is that our discussions of energy do not involve the consumption of energy, but rather the utilization of energy as it changes state. In our day to day lives, energy is not destroyed or created. But we can use it to generate heat and to perform work. And yet! We burn a gallon of gasoline to drive our car and it is gone. What’s going on?
I hope to try and develop a non-technical outline of this in future posts…