Heat transfer rates increase with temperature differences. If the temperature difference between the contenta and the surroundings doubles, the heat movement doubles (for conduction), and so does the rate of temperature change if you’re not dealing with phase change.
For each case, you have to define a starting temp, an ending temp, and a surroundings temp. In both cases we could set the surroundings to 22 C. For the hot case, we could say it starts at 80 C and cools to 55 C. And for the cold case we could start at 1 C and go to 8 C.
In the hot case, we are starting with a 58 C difference and ending with a 33 C difference between contents and surroundings.
In the cold case we are starting with a 21C difference and ending with a 14 C difference.
They may also be assuming an iced beverage in the cold case, and phase change for melting takes a toj of energy.
Not an ELI5-style answer, but I would guess that the cold number includes ice in the mix. Because of that you have a lot more energy to balance out before everything becomes room temperature due to the energy required to change the phase of the ice (solid to liquid). The energy required to make that ice go from 31F to 33F is orders of magnitude higher than the energy needed to go from 33F to 35F, hence the difference. If you were to somehow heat the thermos with high-temperature steam you’d have a similar effect (though not the same) , but would also burn the hell out of your hand when you tried to open the thing.
Guys – it legit has less to do with the temperature differences and even the design of the thermos discussed above. It is A LOT more related to how ice works and that a “cold” drink presumes there’s ice in it.
It takes a lot of energy to convert solid ice to liquid water, and that’s the magic of ice! If you have a non-insulated cup of ice water sitting at room temperature, it will stay “cold” at a constant temperature of 0°C for quite a while, until that last sliver of ice is gone. After that, it will start warming up pretty quickly. If you start with a glass full of ice, at room temperature, you can realistically expect it to stay “cold” for a good hour or two. And that’s with no insulation!
If you have a non insulated cup of hot water, it stars cooling down instantly, and yes, after a little bit of time, it’s no longer considered “hot”.
So the claim is true, but less so because of the thermos’ amazing insulation and a little more because of….ice.
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