Callen H.B - Thermodynamics And An Introduction To Thermostatistics · Problem 2.6-2
SOME FORMAL RELATIONSHIPS, AND SAMPLE SYSTEMS
Physics — Statistical Mechanics · gas-constant-units
Problem
The ``gas constant'' is defined as the product of Avogadro's number (/mole) and Boltzmann's constant . Correspondingly J/mole K. Since the size of the Celsius degree is the same as the size of Kelvin degree, it has the value 8.314 J/moleC. Express in units of J/moleF.Intuitive explanation
The key insight is that unit conversion for temperature differences (or temperature scales used as rates) depends only on the size of the degree, not the zero point. Since a Fahrenheit degree is smaller than a Celsius degree by a factor of 9/5, a rate expressed per Celsius degree must be divided by 9/5 when expressed per Fahrenheit degree—meaning you multiply by 5/9. This is a pure scaling problem: find the ratio between the two temperature units and apply it to the constant.
Intuitive explanation
The key insight is that unit conversion for temperature differences (or temperature scales used as rates) depends only on the size of the degree, not the zero point. Since a Fahrenheit degree is smaller than a Celsius degree by a factor of 9/5, a rate expressed per Celsius degree must be divided by 9/5 when expressed per Fahrenheit degree—meaning you multiply by 5/9. This is a pure scaling problem: find the ratio between the two temperature units and apply it to the constant.