Heat and Work

Energy manifests itself as either heat or work.  And that’s it (we will ignore the mass-energy equivalence described by Einstein.)

Furthermore, energy is always conserved – it is not created or destroyed, ever.

The first sentence tells us a couple of things.  First, since heat and work are both energy, then they must have compatible units of measurement.  And that is indeed correct.  Watt-hours can refer to heat, or Watt-hours can refer to work.

The first sentence in conjunction with the second sentence tells us something much more profound.  If heat and work are both manifestations of energy, and if energy is always conserved, then there must be a fixed relationship between heat and work.

This is not obvious, but it is true.  And it is captured in the “mechanical equivalent of heat” which relates work and heat unambiguously at approximately 4.2 Joules per calorie.  A Joule, by the way, is the the work expended in applying a force of one newton through a distance of one meter.  A calorie is the heat needed to raise 1 gram of water by 1 degree C.

As an aside, you may recall that a newton is roughly 1/4 of a pound and a meter is roughly a yard.  So the work of lifting an apple over your head is the energy to heat up a gram of water by one degree.  Though you would need to deduct the work involved in raising your arm somehow…

The second sentence also says something very odd to energy engineers.  You cannot conserve energy.  If energy cannot be created or destroyed, then conservation (if by this we mean reduced use) doesn’t really have a meaning.  Perhaps energy husbandry would  be a better word.  Or perhaps we are saving something other than energy itself, something about the energy (which is the case), but energy savings do not really occur.

Now, to someone who spends $40 putting gasoline into his car each week, who burns that gasoline to release it’s stored energy, and who sees the gas gauge go down over time as they drive, it sure looks like they are consuming energy.  So what’s going on?

Well, we know some of the energy  goes directly to heat.  Our engine heats up, our exhaust gas is hot, and in the winter we may use the heater, as well, which pulls heat off the engine block.  But what about the work of driving?  We drive, we stop.  What’s going on with that energy?  Why should it “go” anywhere?  Didn’t burning gasoline simply get us from here to there?

The answer is no.  All mechanical work eventually degrades to heat.  Take our car example.  When we are driving, we are pushing against air molecules and overcoming resistance with our tires.  These subtly warm up the air and the road.  So too the automobiles noise, which causes vibrations in the air, and the slightest, basically imperceptible increase in temperature.  All the work the car does eventually turns to heat  (yes, it’s true that if you park on a hill you have some gravitational potential energy saved, but let’s ignore that for the time being.)  Let me say that more unambiguously.  All of the fuel heat you put in your car and combuse eventually returns to the atmosphere as heat.  Work is not “stored”, it becomes, in time, heat.

An energy engineer does not generally concern him/herself with the equivalence of work and heat.  But it is worth keeping in mind that all mechanical energy is ultimately doomed to become what I will call “low grade” heat.  And that, if the amount of generated heat is lessened, we have somehow decreased the degradation of high-quality energy (such as that stored in gasoline) into low grade heat.  But we have not “saved” any energy, not even a single Joule.


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