While reading Gaskell and Laughlin's Intro to ThermoD, I was stuck on something. The relevant passage is:
"In 1802, Joseph-Luis Gay-Lussac (1778–1850) observed that the thermal coefficient of what were called permanent gases was a constant. Previously, we noted that the coefficient of thermal expansion, α, is defined as the fractional increase of the volume of the gas, with the change in temperature at constant pressure; that is,
$$α = 1/v * (∂V/∂T)$$
where $V$ is the volume of 1 mole of the gas at 0°C. Gay-Lussac obtained a value of 1/267 for α, but more refined experimentation by Henri Victor Regnault (1810–1878) in 1847 showed α to have the value 1/273. Later, it was found that the accuracy with which Boyle’s and Charles’ laws describe the behavior of different gases varies from one gas to another. Generally, gases with lower boiling points obey the laws more closely than do gases with higher boiling points. It was also found that the laws are more closely obeyed by all gases as the pressure of the gas is decreased. It was thus found convenient to invent a hypothetical gas which obeys Boyle’s and Charles’ laws exactly at all temperatures and pressures. This hypothetical gas is called the perfect or ideal gas, and it has a value of α =1/ . 273 15.
The existence of a finite coefficient of thermal expansion therefore sets a limit on the thermal contraction of the ideal gas; that is, since α = 1 / . 273 15, then the fractional decrease in the volume of the gas, per degree decrease in temperature, is 1/ . 273 15 of the volume at 0°C. Thus, at –273.15°C, the volume of the gas would be zero, and hence the limit of temperature decrease, –273.15°C, is the absolute zero of temperature. This defines an absolute scale of temperature called the ideal gas temperature scale, which is related to the arbitrary Celsius scale by the equation:
T (degrees absolute) = T (degrees Celsius) + 273.15 "
Here how does he conclude that the volume of the gas is zero at -273.15 degree Celsius? Here we are defining the absolute scale so we shouldn't use the concept of absolute 0 to arrive at that conclusion. It can't be experimental because the word "thus" is used indicating a reasoning.
In short I was confused as the very last line of the extract is supposed to be a revelation, but I don't get what we concluded and how.
Kindly excuse the amateurish question and correct me wherever needed.