thermodynamics - How do we know -273.15 centigrade is 0 kelvin?

I am in no way doubting that humans know that -273.15 centigrade is 0 Kelvin. I'm just curious.

Suppose you know only two things:

1. A new scale for temperature known as the centigrade scale, calibrated against the freezing and boiling points of water using nifty glass thermometers (or any other standard thermometer for that matter).


2. Thermodynamics as it was in the mid 1800's - i.e. knowledge that temperature should be a strictly positive quantity.

How do you go from knowing those two things to saying "Aha! I have now inferred that absolute zero-temperature in the modern thermodynamic sense is, on the centigrade scale, at -273.15!"

Answer

I'm not sure how a precise value would have been obtained circa 1800's. Here's how I had my Chemistry students derive an approximate value with simple equipment.

The apparatus is a hollow steel ball about 10 cm in diameter connected to a pressure gauge. Also involved is a thermometer capable of -70 C to 100 C.

The bulb of this apparatus is then immersed in boiling water, ice water and a mixture of dry ice and acetone. The temperature and pressure are recorded for each treatment. Then the presure is plotted versus the temperature. Since P is proportional to T, a linear plot results. When the plot is extrapolated to P = 0, the temperature is reasonably close to -273 C.

Since temperature is a measure of the average kinetic energy of the particles, the thermodynamic temperature should be zero when the particles stop moving. When the particles are no longer moving the pressure should then become zero as well.