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Scientists say that it is impossible to reach a temperature of zero kelvin, because the atoms will stop moving, and the volume of the substance will become zero, But we have reached the pico kelvin temperature, which is almost zero, and there is no difference between it and zero, so why do they say it is impossible? and The laws of physics still work at picokelvin.

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    $\begingroup$ "But what is the difference between zero kelvin and 1 picokelvin?" It's 1 picokelvin $\endgroup$
    – Bob D
    Apr 18 at 22:45
  • $\begingroup$ @BobD ,I mean in the effect. Is one picokelvin that prevents the atoms from stopping moving completely?! $\endgroup$ Apr 18 at 22:49
  • $\begingroup$ The way I see it, in order for the temperature to be 0 K on a substance, there needs to be a thermal heat sink less than 0 K in order for heat transfer away from the substance to make it 0 K. But nothing can be less than 0 K. $\endgroup$
    – Bob D
    Apr 18 at 22:54
  • $\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$
    – Community Bot
    Apr 18 at 22:55
  • $\begingroup$ @OP: "Is one picokelvin that prevents the atoms from stopping moving completely?!" Basically yes. Any non-zero amount is (clearly) not zero. You seem to be asking whether zero is the same as 0.000000000001. These are clearly not the same. Whether or not you consider 0.000000000001 to be "negligible" depends on the specific situation you are interested in. This temperature (0.000000000001 Kelvin) will likely be negligible for many different types of experiments, but not necessarily all experiments. . $\endgroup$
    – hft
    Apr 18 at 22:59

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The difference is that $0$ is not the same as $10^{-9}$. The latter is nearly zero, but it's not zero.

Why does it matter? Consider for example Charles's Law, which says that for gases, $V/T$ is a constant if the pressure is kept constant. If $T = 10^{-9} K$, there's no problem applying the equation. But if $T = 0$, the law breaks down since division by zero is undefined.

This doesn't mean that the laws of physics break down at $T = 0$, after all Charles's Law is just a special case of the ideal gas law which does not break down at $T = 0$. But it does show that $0$ is special and not the same as $10^{-9}$, $10^{-12}$ or any small but nonzero number, and you might need to treat $T = 0$ differently.

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In some thermodynamic contexts, the inverse temperature $\beta=1/T$ is a more meaningful quantity. This makes it more clear that 0 Kelvin, or $\beta = \infty$ is approachable but unattainable. And so in asking about pico-Kelvin being "close enough," you are asking if $\beta = 1,000,000,000$ is "close enough" to $\beta = \infty$. Answer: for some practical purposes, maybe. For others, no.

(Yes, I set Boltzmann's constant equal to 1 for simplicity.)

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