Temperature Change

Heat Raises the Temperature

Time for more assumptions!  In this case, I am assuming that the mass of iron to which the heat energy is imparted will be the material directly beneath the hammer, in the cross section of the metal.  So, I'm going to do two scenarios.  First, how much will the temperature increase with a "perfect" hammer blow when the iron is at its initial size (1/4" round bar) and second, when it is nearly the size of a finished square nail (1/8" square). 

First we need the mass of each hypothetical segment of iron.

Volume of a 1/4" round piece of iron 1" long is:

((.0254/4 m)/2)^2(3.14159)(.0254 m) = 0.000003218 cubic meters

Mass of steel per kg (source): 7850 kg/m^3

Mass of a 1/4" round piece of iron 1" long is: .0252613 kg


Volume of a 1/8" square piece of iron 1" long is:

((.0254/8 m)^2)(.0254 m) = 0.000000256 cubic meters

Mass of steel per kg (source): 7850 kg/m^3

Mass of a 1/4" round piece of iron 1" long is: .002009976 kg


(Almost there!  Hang on a little longer!)

The specific heat (energy needed to change the material's temperature by one Kelvin) of iron is 450 J/kgK (source)

So, energy needed to raise the round bar one K is: 450 J/kgK x .0252613 kg = 11.3676 J

One blow doesn't do much.  It raises the metal by about 1 degree each time I hit it. 

Things get a little better when we get to the square nail shank size.

There, energy needed to raise it one K is: 450 J/kgK x .00201 kg = 0.9045 J

So, at that point, each blow should raise the temperature by almost 14 degrees.  Still pretty unimpressive. 

Let's get a little more precise in our hammering, however.  It may look like a clumsy block of iron on the end of a hunk of wood, but a smith can do some pretty detailed work with that hammer.  I can, on a good day, hit a very small target with a very focused blow.  Let's posit the tip of a nail, at a cross section of 1/16" square and about 1/8" long.  Same hammer blow, same specific heat, how much am I going to heat that little tip up with a blow?

Volume: .000000008 cubic meters. 
Mass: .000062812 kg
Energy to raise it one K: 0.02827 J

Now, we're talking!  That means a perfect blow should raise the temperature by 442 K at that size!  If I even strike a quarter-perfect blow, I am going to raise the temperature enough to really see it go from dull red to bright yellow.  Considering that any experienced smith can judge temperature by eye within less than 25 degrees or so (always relative, not empirical - the light in a shop changes from one minute to the next if sun is coming in a window, I'm just talking about judging  available working heat relative to "fully hot" iron), this sort of magnitude of temperature change should be very clear to see. 

(Which is the case, actually...)

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