What is the temperature at which all particle motion of matter ceases? a. absolute zero b. melting point c. boiling point d. heat of fusion

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Well, to answer this question. We need to know what each of those are.

Melting point is the point at which a solid and liquid state are in equilibrium. In the solid state (at certain temperatures...) particles are virbrating in place, more or less. In the liquid state, particles are constantly becoming associated with different other particles, indicating they're in motion, too.

Boiling point is the point at which liquid and gas are in equilibrium. In a similar way to the above situation, gases and liquids are both constantly in motion.

Heat of fusion is the heat released or absorbed by a substance during the transition from solid to liquid or vice versa. It is not a temperature.

Clearly, B, C, and D are wrong.

So what is A, anyway?

Before Kelvin made his temperature scale, the temperature scales being used had arbitrary zero points. 0 degrees Celcius is simply the freezing point of pure water. 0 degrees Fahrenheit is going to be the freezing point of saltwater.

Kelvin wanted his scale to be more meaningful  that relating temperature to some arbirtrary point. He ended up creating a scale using thermodynamics that predicts the lowest possible temperature: absolute zero or zero degrees K.

To see why we know this is the lowest temperature possible, we just look at the fact that temperature is related to kinetic energy of a substance. The higher the temperature, the higher the average kinetic energy. It stands to reason, then, that there will be a temperature at which there is zero kinetic energy. With zero kinetic energy, there is no motion. There is no such thing as negative kinetic energy, of course. So, Kelvin set his zero point to be the temperature at which there is no kinetic energy in a substance. Therefore, at absolute zero, there is no motion.

Of course, we will likely never reach absolute zero (due to even the coldest things in the world still radiating heat to the object we're trying to bring down to that temperature). However we've gotten close! There's a special form of matter called Bose-Einstein Condensate that only exists at extremely cold temperatures. In fact, the record is set by a BEC made at MIT of sodium atoms found to be at 450 +/- 80 pK (pK = 10^-12 K). It's still not zero, though!

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