Fourth Mundane Reality: The Massic Heatability (Specific Heat Capacity) of Water

Table of Candidate Massic Heatabilities

In order to derive Primel's coherent unit of temperature, as well other thermodynamic units, Primel starts by selecting a coherent unit for massic heatability (aka specific heat capacity).  This quantity measures the intrinsic capacity for a given material to undergo a temperature change in response to the addition or removal of a given amount of heat, per unit mass of the material. As in the case for density, Primel recognizes water as a representative material in the human environment, and a substance vital for human life. Therefore, the capacity of water to be heated and cooled constitutes Primel's fourth "mundane reality".

Temperature is a quantity proportional to the statistical average kinetic energy of the random motions of the microscopic constituents of a system. Heat is a form of energy transfer, just like mechanical work, but involving this kinetic energy of microscopic constituents. Heatability (aka heat capacity) of an object expresses the ratio of the heat added to or removed from it, to the temperature change induced on it.  Massic heatability (aka specific heat capacity) of a material expresses its heatability per unit mass of the material. (Heatability is an extensive property of systems; massic heatability is an intensive property of materials.)

Experiments by James Prescott Joule and others in the 1840's_d|1090's_z established the mechanical equivalence of heat and work.  But this understanding came only after units for temperature and heat had already been devised on an ad hoc basis. The Fahrenheit degree or Rankine degree, and the Celsius degree or kelvin had been selected with the purpose of making their scales convenient.  Units of heat such as the calorie, the kilocalorie, and the British thermal unit (BTU) were derived in terms of these temperature units, without attempting to make them coherent with mechanical units.

For instance, the Celsius degree (or kelvin) was selected as a temperature unit solely for the convenience of making the scale from the freezing point of water to its boiling point exactly 100_d units. The kilocalorie is the amount of heat transfer needed to raise (or lower) the temperature of 1 kilogram of water by 1 degree Celsius (or 1 kelvin). The joule, on the other hand, represents the amount of work needed to accelerate that same 1 kilogram at 1 meter/second² across a distance of 1 meter. It turns out that the kilocalorie is approximately 4200_d times larger than the joule, a difference of more than 3 and a half orders of (decimal) magnitude. This demonstrates the fact that heat is a rather more concentrated form of energy than mechanical work.  But it also highlights how conventional unit systems lack coherence in relating thermodynamic units to mechanical units. If SI had derived its unit of temperature based on what one joule of heat would do to a kilogram of water, rather than what 4200_d joules would do, then this would eliminate the arbitrary factor and make the system more coherent. This would necessarily make the hypothetical unit of temperature some 4200_d times smaller than a Celsius degree, so scaling up to the kilo·unit (or perhaps the myria·unit) would be more practical for everyday use.

That is the approach Primel follows.  Primel recognizes that its coherent unit of heat, the ⚀heatel, and its coherent unit of work, the ⚀workel, are one and the same; both are just synonyms for its coherent unit of energy, the ⚀energel. Primel arrives at its coherent unit of temperature, the ⚀temperaturel, by noting that its unit of heatability, the ⚀heatabilitel, would equal 1 ⚀heatel per ⚀temperaturel; and its coherent unit of massic heatability, the ⚀masselic·heatabilitel,  would be 1 ⚀heatabilitel per ⚀massel. Primel then selects a representative value for the massic heatability of liquid water as its ⚀masselic·heatabilitel. The resulting ⚀temperaturel turns out to be tiny, but scaling this unit up by four orders of dozenal magnitude, to the ⚀quadqua·temperaturel, provides a practical unit for everyday use. 

By the equivalence of work and heat, the heat required to induce a 1 ⚀temperaturel change to any mass of water is equivalent to the work needed to raise that same mass of water by 1 ⚀lengthel against Earth's gravity. Since Primel colloquializes the ⚀lengthel as the ⚀morsel·length, it is apt to colloquialize the ⚀temperaturel as the ⚀morsel·temperature. This underscores just how tiny a quantity of temperature it is.  Similarly, the heat required to induce a 1 ⚀quadqua·temperaturel change to any mass of water is equivalent to the work needed to raise that same mass of water by 1 ⚀quadqua·lengthel against Earth's gravity. Since Primel colloquializes the ⚀quadqua·lengthel as the ⚀stadial·length, it is apt to colloquialize the ⚀quadqua·temperaturel as the ⚀stadial·temperature, or more succinctly as the ⚀stadegree.  The notion that heating something by 1 ⚀stadegree (approximately 0.4_d kelvin) is equivalent to lifting it on the order of an Olympic stadium into the air, underscores just how concentrated a form of energy heat actually is.

The massic heatability of water varies appreciably with temperature (as well as other factors) from a minimum of about 4179_d joules per kelvin per kilogram, to a maximum of about 4220_d joules per kelvin per kilogram, with a mean value over water's liquid range of about 4190_d joules per kelvin per kilogram. Theoretically, any value within this range is a candidate for Primel's standard value. 

For convenience, Primel chooses the value for its ⚀masselic·heatabilitel so that the range from the freezing point to the boiling point of water is exactly a dozenally-round 190_z|252_d ⚀stadegrees. This puts the ⚀masselic·heatabilitel at 4198.76286389748_d joules per kelvin per kilogram. This is a bit above the mean value for water, but slightly under the value of 4204_d joules per kelvin per kilogram which occurs at 4°C, near water's maximum density. This puts the ⚀temperaturel at ≈ 0.49186ᘔ35×10⁻⁴_z|1.91370272388791×10⁻⁵_d kelvin, or 0.86ᘔ351×10⁻⁴_z ≈ 3.44466490299824×10⁻⁵_d degrees Fahrenheit, and the ⚀quadqua·temperaturel or ⚀stadegree at exactly 5/7 of a Fahrenheit or Rankine degree (0.714285_d|0.86ᘔ351_z °F), or exactly 25/63_d|21/53_z of a kelvin or Celsius degree (0.396825_d|0.49186ᘔ35_z K). Primel makes this choice solely in order to make temperature conversions between Primel units and conventional units relatively simple rational numbers that may be computed exactly.  It should not be taken to imply that Primel units are in any way "based" on conventional units.

(Tom Pendlebury took a similar approach when he derived the Calg, the coherent unit of temperature for his TGM metrology. He chose his masselic·heatabilitel, the Calsp, in such a way that 1 biqua·Calg (colloquialized as 1 bigree) equals exactly one decikelvin (0.1_d kelvin, or 0.18_d °F), and 1 triqua·Calg (colloquialized as 1 tregree) equals exactly 1.2_d kelvin (or 2.16_d °F). This was solely in order to make conversions to conventional units simple and exact, and does not imply that TGM's units are "based" on the decikelvin. However, that choice does set the Calsp to a value (about 4177_d joules per kelvin per kilogram) just under the minimum for the natural range for water, making for a slightly uneasy compromise. A close approximation of the bigree in Primel would be the ⚀quarter·stadegree aka the ⚀colossal·temperature or ⚀colossegree (exactly 5/28_d|0.17857142_d|0.286ᘔ351_z °F, or exactly 25/252_d|0.09920634_d|0.1235186ᘔ_z K). Primel would approximate the tregree with the ⚀trina·stadegree aka the ⚀turrial·temperature or ⚀turregree (exactly 15/7_d|2.142857_d|2.186ᘔ35_z °F

Primel provides three temperature scales based on the ⚀stadegree, with different choices for a zero point:

• A ⚀stadigrade·absolute scale, zeroed at absolute zero, analogous to the kelvin and Rankine scales.
• A ⚀stadigrade·crystallic scale, zeroed on the freezing point of water, analogous to the Celsius scale.
• A ⚀stadigrade·familiar scale, zeroed on 40_z ⚀stadegrees below freezing, analogous to the Fahrenheit scale.