Just how old is a 45 year old soup (and would you eat it)

On my absurd podcast Cheese & Weather we covered a topic Jason Beggs has been requesting: what do we think of this soup that has been continuously simmering for 45 years? Since that article was written in 2019 it's actually a 50 year old soup!

I'll let you listen to the podcast to hear our take, but I was wondering: is there a single molecule of the soup that went into the pot in 1974? That's 18,250 days of selling the soup, keeping "a little bit" for the next day, and diluting it. That's a huge amount of dilution, but on the other hand - there are an astronomical number of molecules in a single spoon of soup, let alone a cauldron.

So let's figure it out. That article describes a large pot, 5 feet in diameter, 2.5 feet tall. Such a pot would contain 367 gallons if it was a perfect cylinder and full to the brim - let's reduce it by 10% and assume 330 gallons. That's 1,249 liters or 1.249 × 10⁶ cm³.

Let's assume the cauldron is full of water, and only water - the tradeoff is that the density of the different ingredients, and the broth itself, is approximately but not exactly the same as the density of water. The density of water at the boiling point is 0.95837 g/cm³.

0.95837 g/cm³ × 1.249 × 10⁶ cm³ = 1.197 × 10⁶ g of H₂O

So how many molecules are in 1,197 kg of H₂O?

The molar mass of H₂O is 18.015 g/mol, so 1.197 × 10⁶ g / 18.015 g/mol = 6.644 × 10⁴ mol of H₂O.

Using Avogadro's number we can calculate the number of molecules:

6.644 × 10⁴ mol × 6.022 × 10²³ = 4.001 × 10²⁸ molecules

So that's a lot of molecules. For some scale, the universe is 13.8 billion years old, which is 4.3 × 10¹⁷ seconds. Nowhere close!

So what percentage of the soup remains after 50 years, or 18,250 days of saving "a little bit" of the soup? Let's assume that they keep just 1%, or 3.3 gallons, each day. After one day, 1% of the original soup remains. After two days, 0.01% of the soup remains. After one week, just 0.00000000000001% of the original soup remains. After 50 years, 0.01¹⁸²⁵⁰ remains, or 10^-36498%. That is a vanishingly small number that completely dwarfs the large number of molecules.

In fact, I'm not even sure that a single molecule remains after 15 days! After 15 days 0.01¹⁵ or 10^-30 remains. 4.001 × 10²⁸ molecules × 10^-30 = 0.04 molecules. Not many molecules.

So yeah, you're not eating 50 year old soup. At most, it's about two weeks old. Which is definitely longer than the 2 hours the FDA recommends for perishable foods, so let's hope they've kept it above 140 °F.

Bon appetit!