what if your stick is at absolute zero? your molecular movement would then be stopped. would the stick finally be able to move instantaneously?

When you add salt to ice+water the temperature decreases. Your misconception is that somehow energy is being removed from the system.

Melting is endothermic in either the + salt case or the -salt case, so it should be a wash in the final consideration of temperature changes.

The thing is, we can see similar things with roughly 1 meter wooden sticks: baseball bats. This article talks about how hitting home runs when the bat breaks at the handle (or even "hitting" home runs when you've let go of the bat) aren't much different from a regular home run from the ball's perspective, because the wave is still traveling down to where the bat will break by the time that the ball leaves contact.

Which part isn't true?

This is not true. You can do the kitchen experiment yourself.

if you apply force on an object - technically, you only apply that force on the outermost layer of atoms. so you push the outermost layer against the next layer, which itself pushes on the next layer and so on.

there is a maximum speed with which that force can propagate through the object. it is the speed of any pressure wave. the most common pressure wave is a sound wave - so usually, we call this speed the speed of sound. in a rigid object, sound is much faster than in air. the actual value for this speed is dependend on the material. if you have a wooden stick for example, if you push on one end, that force is transmitted through the wood with a speed of about 3500 to 5000 meters per second. which is quite fast.

if your stick is about one meter long and you push on one end, that force can be transmitted fast enough, that it looks as if that force is transmitted instantaneous. you can't push that stick fast enough to notice any delay. therefore the only force you have to apply is that to move the stick itself.

however - if your stick is considerably longer, you notice that delay between your push on the one end and the movement on the other. the stick can't move away fast enough. so you have to compress the stick - or apply the force very slowly. if you compress the stick, you have to apply extra force - you not only have to move the mass of the stick (which is now very high). if you push slow enough, you only have to compress the stick a little bit before that pressure can move through the whole stick.

now take a stick that is long enough to reach to our moon. our moon is about 400 000 kilometers away. the speed of sound in wood is about 5 kilometers per seconds. so - if you push on one end of that stick, it takes about 22 hours (!) until the other end moves. if you push the stick about 10 cm on one end, you have to compress the wood - which takes quite some force. but never mind - that stick would be so heavy that moving it at any speed is an astronomical feat.

have you ever seen a stick of wood about one kilometer long? me neither. no wonder, all of this is not quite intuitive.

"Give me a place to stand and with a lever I will grunt and strain to no effect." -- Archimedes (kind of)

But if the ice and the water are all at 0⁰ C, then they're going to stay at 0⁰ C no matter how much salt you pour in.

The only way the water goes below 0⁰ C is if the ice starts below zero.

This would be similar to pushing a, say, 100m stick against a concrete wall since the inertia of a stick multiple LYs in length would be comparable. Sure, you could push the end 10cm, but it would just crumple or bend.

Fun with math: If the 'stick' was a steel rod about a cm square, it would weigh around 7,400,000,000,000 tonnes per light year. That's only 1/10,000,000th the weight of the moon, but it's still substantial.

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No the melting is endothermic.

>just adding salt can't take energy out of the system

The temperature decreasing does not mean that the total energy of the system has changed. There is an energy transfer between kinetic energy and potential within the system.

Only really in an ideal gas system does the temperature relate to the total energy.

Energy is conserved. The thermal, kinetic energy of the ice and water is transferred to the potential energy in the bonds of the ice (to break them).

The temperature of a system is only ever directly related to the total energy of a system for an ideal gas.

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Before calculus you probably took a class where you did lines (slope/intercept form, etc), right? Think about all the word problems where you wanted to know the slope of the line- when you wanted to know "rate of change" or "how much more it costs to build one more object" or anything like that. All of those types of problems require calculus if you want to do them for anything more complicated than a line.

As an example- perhaps you had a problem like this:

> A car is traveling down a race track in a straight line. At t=10 seconds it's 100 meters down the track, and at t = 20 seconds it's 150 meters down the track, how fast is it traveling? Where did it start on the track?"

So, you find the slope and intercept of the equation, and say "oh, it's traveling at 5 m/s, and it started 50 m down the track.

But if the car isn't traveling at a constant velocity, instead you say "at t = 0 seconds a car starts from rest and is 100 m down the track. At t = 10 seconds, he's 200 meters down the track, and he was accelerating the entire time. How fast is it traveling 2 seconds after it starts to accelerate?" well now you need to use calculus. You need to find the slope of the tangent line to the equation that describes his position. You hear physics terms a lot because in general, velocity is the derivative of position, and acceleration is the derivative of velocity (aka- the tangent line to the position graph is the velocity, and the tangent line to the velocity graph is the acceleration, just like the slope of a line in a linear graph is the velocity).

Classical physics cannot describe quantum physics- but quantum physics can replicate classical. The main reason we don't use quantum physics in the classical realm is because it's far too mathematically challenging for large systems.

This Q&A might be helpful for a better understanding.

It's not quite right to say that "time stops at the speed of light." It's better to say "time becomes undefined at the speed of light." But what's interesting is, so does length due to length contraction. So using layman's terms, you could say time stops, but also, it doesn't have to go anywhere, because lengths are all zero.

Dark matter was originally theorized to explain discrepancies between scientific predictions and measurements. But it turns out, it has predictive power. When we estimate the amount of dark matter we think there must be in the universe, it actually explains the relative amounts of Hydrogen and Helium we see in the universe now.

Apparently it was junk they ejected. It will enter the atmosphere soon to burn up.

>The resulting water is colder than the ice it came from and the water conducts heat better than ice, so the water warms up quickly until it gets warmer.

Thanks for this sentence. I couldn't get my head around how if something was colder it could still reach room temperature fasters than something warmer since the colder thing has to pass the warmer thing's temperature to get there. In my head it was the equivalent of "you can accelerate faster if you start rolling backwards".

For the singular purpose of human habitation, not really. Unless we find significant resources on other moons or planets and their value outweighs the cost of extraction, even with better space travel and hauling, the danger of living on extraterrestrial bodies remains. Space is dangerous even with the best technology - our science fiction even includes this quite often where breaches to spacecraft or colony buildings leads to disaster.

That being said if research was the main goal and we could justify the cost of it then the icy moons of Saturn and Jupiter, notably Titan, Enceladus and Europa would be the best targets if you care about discovering life as they are most likely to harbor it.

True, and now the entire surface area of the water is cooling the environment faster at a lower temperature.

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