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Temperature Scales
"Temperature" intends to describe a material's hotness property
Humans' sense of touch is not too bad at ranking items by how hot they are at any one time,
but we're not very good at remembering these sensations,
. . . and our judgements can be muddled by having recently been in colder or hotter environments.
Because one's hands become hotter if they are rubbed together
as they do Work to each other, their motion Energy is dissipated by friction.
Energy that is displayed as directed motion is usually called "Kinetic Energy"
− the 3 independent directions can each hold KE, but Energy itself is not directional.
. . . Their obviously higher temperature must've been accompanied by some sort of Thermal Energy
(which came from the KE which was converted to TE by friction).
. . . A thermometer measures some aspect of this Thermal Energy,
but thermometers are calibrated according to a Temperature scale.
There are two temperature scales in common use around here: degrees Fahrenheit and degrees Celsius.
. . . these peculiar "degree" adjectives before the units implies that these scales do not have their zero-mark anywhere near the actual zero of temperature,
so any item has a lot of Thermal Energy even at (either) "zero" temperature.
Daniel Fahrenheit chose his scale's "0" as the coldest that water-ice would get when mixed with salt.
32 °F is the mixture of solid water and liquid water (ie, freezing/melting)
98.6 °F is a healthy human's internal body temperature
212 °F is liquid water boiling at standard atmospheric pressure.
. . . Notice that there are 180 F° from water melting, to water boiling
(this difference is not called 180 °F because it is relative to water freezing, not the °F scale's zero-point).
The modern Celsius scale chooses its "0" as water's freezing/melting;
100 °C is liquid water boiling at atmospheric pressure.
... (Anders Celsius originally had the 0 and the 100 marks reversed, as a "coldness" scale);
... (Jean-Pierre Christin, and months later Carl Linneaus, set it upward as a hotness scale)
. . . There are 100 C° from water melting to water boiling, so it used to be called the "Centigrade" scale
(each Celsius degree is comparatively coarse).
⇒ each unit Celsius degree is 1.80 Fahrenheit degrees.
The −32 F° from freezing to the ice-salt mix would be
−32 F° × 1 C°/1.8 F° ≈ −17.78 C°
so the ice-salt mix (defining 0 °F) would be −17.78 °C ... relative to 0 °C at water freezing.
Because the Celsius scale is so much coarser that the Fahrenheit scale, it catches up (down?) a bit colder than this
−40 °C is −40 C° from freezing (negative meaning below), so that would be
−40 °C × 1.8 F°/C° = −72 F° from (below) freezing
... since freezing is 32 °F , −72 F° + 32 °F = −40 °F ... the same number on the other scale.
We will see another Temperature scale (or two) after we explore how these temperatures are related to Thermal Energy.
Thermometers
Early thermometers tried to quantify temperature (make it a quantity) by matching a number to each temperature.
Condensed matter expands slightly at higher temperature and contracts slightly at lower temperatures.
a typical solid expands in each dimension, about 5 to 100 parts per million per degree;
... different materials expand different percentages.
Bi-metal strip : 2 different metal strips fastened back-to-back when straight, will curve at another temperature.
brass expands almost twice as much as iron, so will be on the outside of the curve at high temperature
but at the inside of the curve at low temperatures.
longer metal strips curve more (but cost more to make) - thinner metal strips curve more (and cost less).
Bi-metal thermometers are compact enough to fit easily in an oven, if the long strip is curled into a spiral.
liquid-in-glass thermometers allow a fluid in the thermoimeter bulb to expand at higher temperature,
since a (pyrex) glass bulb expands in Volume about 10 ppm per degree (other glass expands about twice as much)
while mercury expands 180 ppm per degree, and ethyl alcohol expands 750 ppm per degree.
... these liquids might fit in the bulb at −40 °C, but not at higher temperatures.
Suppose a pyrex thermometer bulb has Volume = 1.000 000 mL at −40 °C ... just filled with mercury.
at −39 °C the glass will hold 1.000 010 mL ... and by 0 °C it will hold 1.000 400 mL
but the mercury will occupy 1.000 180 mL −39 °C and at 0 °C will need 1.007 200 mL !
... (original Volume × 10/1000 000 [1/C°] × 40 C° )
The 0.006 800 mL excess mercury (= 6.8 mm³) goes into a very narrow expansion tube ...
... if the tube is 1mm × 0.1mm , the mercury would fill 68 mm of the tube ! alcohol almost 4× as far.
Notice that these thermometers are only recognizing changes in Length or Volume relative to their Lengths or Volumes at another Temperature.
. . . it is not obvious that Nature has a "lowest" possible temperature
- a "correct" temperature scale should have its zero-mark for items that have zero Thermal Energy.
Temperature is Thermal Energy per atom motion - an intensive quantity
When you mix hot water with an equal amount of cold water, the temperatures do not add -
so temperature cannot be an extensive quantity.
. . . Instead, the temperatures average, indicating that temperature is some kind of an intensive quantity.
. . . An intensive quantity is the ratio of two extensive quantities (e.g, ρm = m/V).
An intensive quantity combines via a weighted average,
weighted by whatever the divisor is in its defining ratio : (e.g, ρm,total = [ρm,1 ×V1 + ρm,2 ×V2] / [V1 + V2] ).
. . . When a small amount of hot water is mixed with 3× as much cold water, the small amount changes its temperature (downward) 3× as much as the large amount changes.
But which extensive quantity is the divisor? ... The large amount of water has 3× the mass, but also 3× the Volume, but also 3× the number of atoms
... we must use other substances (besides water), to see what the actual divisor is, for temperature.
If we place hot iron into cold water, the cold water temperature rises.
This indicates that temperature does measure relative Thermal Energy concentration.
. . . If we use an equal mass of hot aluminum (compared to the iron), the cold water temperature rises twice as much.
The aluminum block carried 2× the amount of Thermal Energy to the water, so mass is not the correct divisor ...
This aluminum block has 2.9× the iron block's Volume, so Volume is not the correct quantity either ...
but the aluminum block has 2.0× the number of atoms ... an iron atom has 2× the mass of an aluminum atom. (but only 71% as much Volume).
⇒ temperature is trying to be (Thermal Energy) / (number of atoms) ... with some zero offset.
Thermal Energy per atom, or per molecule?
Let's compare the aluminum's Thermal Energy to water's Thermal Energy:
. . . each aluminum molecule is one aluminum atom ... it has (27/(2+16) =) 1.5× as much mass as a water molecule.
but adding aluminum to an equal mass of liquid water, the aluminum's temperature change is 4.65× as much as the water's ΔT .
. . . it is very tempting to notice that, since each water molecule is made from 3 atoms [HOH] ,
an aluminum atom has (1.5×3 =) 4.5× the average atom in the water sample.
⇒ Thermal Energy seems to be essentially proportional to the number of atoms.
But wait - solid water (ice) has twice the temperature change that liquid water has
when aluminum blocks are added to equal water masses, in each phase.
. . . The difference is that the liquid molecules can rotate, while the ice molecules cannot.
so half the atom motions that occur in liquid water, ice atoms cannot do.
⇒ Thermal Energy changes depend on material details, not just the constituents in the substance.
specific Thermal Energy per degree: abbreviated c (lower case)
Because it is so easy to measure a sample's mass precicely, it is traditional to
collect all the details about atom mass, and possible atom motions,
into an experimentally-determined intensive quantity that uses mass as its extensive divisor.
(recall: an item quantity [TE] that has been divided by the item mass is called "specific quantity [TE]")
⇒ c = [ ΔTE / ΔT ] / m ... traditionally called the material's "specific heat capacity" (poor vocabulary choices - sorry)
. . . these are measured by STEM laboratories, results available for most materials (at least near room temperature).
they are essentially constant with temperature, except near phase changes.
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