alcoholometry-core

A TypeScript implementation of International Organization of Legal Metrology (OIML) publication r022-e75.

Overview

This library exports two function density and massFraction.

• density is computed in kg/㎥ with respect to the mass fraction ethanol in solution expressed as a number between 0 and 1 and the temperature in degrees Celcius as per the formula on page 12 of r022-e75.
• the massFraction, given a density and temperature is computed using the Newton-Raphson method on the density function.

Usage

Install

$ npm i alcoholometry-core

Load

const { density, massFraction } = require('alcoholometry-core');

or

import { density, massFraction } from 'alcoholometry-core';

Use

let p = .73 // mass fraction of ethanol solution, should be between 0 and 1, inclusive
let t = 15.5 // temperature in °C, should be between -20°C and 40°C for formula to be valid
let d = 901.42 // density in kg/㎥, should be between  771.93 kg/㎥ and 999.97 kg/㎥ for result to be valid

console.log(density(p,t)) // prints 864.2486339111406
console.log(massFraction(d,t)) // prints 0.5709979995228677

Errors

massFraction will throw an error if the underlying implementation of the Newton-Raphson method fails to converge within 20 iterations. Assuming that the density and temperature fall within the appropriate bounds, convergence can be essentially guarenteed (see Valid Ranges for details).

Building

$ git clone https://github.com/alpacahaircut/alcoholometry-core
$ cd alcoholometry-core
$ npm run build

Testing

$ npm test

Physical Considerations

Pressure

density does not account for ambient pressure. Functions only model physical solutions at standard pressure.

Valid Ranges

While the density function is perfectly well defined for all input values, to obtain physically meaningful and valid result values should fall in the following ranges:

• mass fraction represented as a decimal, should be, by definition, between 0 and 1 inclusive.
• temperature per r022-e75, should be between -20°C and 40°C, inclusive, to produce valid results.
• density (for massFraction) should be between 771.93 kg/㎥ (density of pure ethanol at 40°C) and 999.97 kg/㎥ (density of pure water at 4°C), to produce valid results.

However, staying within these ranges does not necessarily correspond to a physically meaningful state. For example water (p=0) experiences a phase change at t=0, and so density(0,-5) does not produce a density for any realizable state of matter at standard pressure. Similarly we can obtain anomolous results with the massFraction function as the following code snippet shows:

console.log(massFraction(775.42, 15.2)) 
// prints 1.0514165233724417

Moreover, convergence of massFraction is not gauranteed outside of the above ranges for density and temperature or even for non physically realizable combinations thereof and may throw an error:

massPercent(200,20);
//Error: [alcoholometry-core] massPercent failed to converge within 20 steps. Are d and t in the appropriate ranges? See https://github.com/alpacahaircut/alcoholometry-core#README.md for details.

// minimum density of an ethanol solution at -19.9°C 
// occurs with pure ethanol and is roughly equal to 823.04 kg/㎥
massFraction(810,-19.9);
//Error: [alcoholometry-core] massPercent failed to converge within 20 steps. Are d and t in the appropriate ranges? See https://github.com/alpacahaircut/alcoholometry-core#README.md for details.

Our tests indicate that most non-convergence occurs at or around -20°C and one can be confident in congvergence if at least one of the following conditions are met

• temperature is greater than or equal to -19.0°C (and all of the other above restrictions are met)
• density is greater than or equal to 818 kg/㎥ (and all of the other above restrictions are met)

See tests and Testing.

Agreement with experiment

Discrepencies between the OIML density function and experimental results are discussed in r022-e75 for values within the above described ranges.