What is happning with phase changes and intermolecular forces

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kjamha
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When a substance undergoes a phase change from a solid to a liquid the substance can absorb heat energy without undergoing a temperature change. But I also read that when a substance melts, the atoms absorb energy and thereby vibrate faster, overcoming the intermolecular forces. Temperature is defined as the average KE of random translational motion of atoms/molecules of a substance.
So if molecules vibrate faster in overcoming intermolecular forces, wouldn't the temperature go up? This contradicts the fact that temperature does not go up during a phase change. Can someone shed some light on this? I'm thinking there is a lot more to phase change on a molecular level. Thanks!
 
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kjamha said:
Temperature is defined as the average KE of random translational motion of atoms/molecules of a substance.
No, it is not defined like that. This is just a simple picture of what goes on inside a substance when the temperature changes.

kjamha said:
So if molecules vibrate faster in overcoming intermolecular forces, wouldn't the temperature go up? This contradicts the fact that temperature does not go up during a phase change.
Exactly! The conclusion is that saying that T = KE is incorrect (or incomplete).