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Well, the temperature profile of an object on the macroscopic scale is governed by, $${{dT} \over {dt}}=\kappa \cdot \nabla^2 T$$ Where T is the temperature, t is time, and $\kappa$ is the thermal diffusivity. It's the constant that matters here. The larger the constant, the faster the temperature changes. The equation itself is called the Heat Equation. ...

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Yes space is a vacuum which means no pressure and air and no gravity. As you said ice melts quickly in high pressure so in space ice will take a longer time to melt if it's not so hot there.

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Water, like most liquids does indeed get more viscous as its temperature approaches freezing point. See the graph below, which I took from the "Engineering Toolbox" However, what's interesting about this curve is that it does not diverge as $T\to 0^\circ{\rm C}$. The reason is that a phase change really is for all effective purposes a discontinuous ...

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Polymers such as wax definitely undergo phase transitions. You inquired about paraffin wax, which is oil-based. Paraffin wax is made of long rod-like molecules called linear straight-chain alkanes. It's solid at room temperature, but when refined as liquid paraffin and combined with water, it can act as liquid crystal, which complicates its phase diagram. ...

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