is beehaw related to lemmy?

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Cake day: June 8th, 2023

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  • As someone who is often unable to even enjoy soda because it immediately starts bubbling up and only remains as a sugary liquid by the time it reaches the esophagus, I guess I can’t replicate your observations. Also, I guess I need more water in my mouth before I can let Jesus into it (for a more pleasant experience for both of us)






  • Goddard Guryon@sopuli.xyztoLemmy Shitpost@lemmy.worldPanik
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    1 year ago

    Indeed, an integer is divisible by 3 if and only if the sum of its digits is divisible by 3.

    For proof, take the polynomial representation of an integer n = a_0 * 10^k + a_1 * 10^{k-1} + … + a_k * 1. Note that 10 mod 3 = 1, which means that 10^i mod 3 = (10 mod 3)^i = 1. This makes all powers of 10 = 1 and you’re left with n = a_0 + a_1 + … + a_k. Thus, n is divisible by 3 iff a_0 + a_1 + … + a_k is. Also note that iff answers your question then; all multiples of 3 have to, by definition, have digits whose sum is a multiple of 3







  • Paint it as a chemical reaction in order to understand its equilibrium state. We basically have:

    H2O (gas) ⇌ H2O (liquid)

    By sealing the jar with the water already boiling, we initialize the system to be in a state with equal(ish) amount of both liquid and gas. Then we allow the system to cool down so that the liquid water is no longer boiling. Now the system sits at an equilibrium between liquid and gas states.

    Now, when we put ice on top of the jar, the water vapor condenses and gets converted to liquid, pushing the equilibrium to the right. But this decreases the overall pressure in the system since fewer particles now occupy the volume above the liquid’s surface. This is essentially the system trying to pull itself back towards the original equilibrium i.e. towards the left of the equation, which it does by making more water vapor i.e. boiling.

    This reaction-like picture helps in visualizing the system better in some cases, so I tried to add it alongside the pressure dynamics scenario. You may be interested in Le Chatelier’s principle if you prefer this.


  • When the water vapor inside the jar comes in thermal contact with the ice outside, it condenses and precipitates. This decreases the vapor pressure inside the jar, which then causes the water to boil.

    Boiling is not just a temperature-based phenomenon, it’s also a pressure-based one: a water body maintains an equilibrium between liquid water and water vapor right above its surface. If you remove the water vapor from above the surface, it decreases the vapor pressure and shifts the equilibrium away from the liquid state, which is essentially boiling. Note that this is different from evaporation since the liquid water is not using heat from an external source to vaporize. You can also see this in daily life, for example, in that water boils at a different temperature on mountains due to pressure difference.