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When heat is supplied to water, for example, the temperature of water increases with the rise in heat energy but when the temperature reaches $0^\circ$centigrade or $100^\circ$centigrade, the heat energy is used to counter the intermolecular force and the temperature remains constant until all the ice has converted to water or all the water has converted to vapour. My question is that why is the heat energy not used to counter the intermolecular force when the temperature is not at melting or boiling point? Why does the vibration or the temperature keep on increasing even if the intermolecular force is not countered?

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    $\begingroup$ You don't need 100 C to break molecular bonds. Liquid water evaporates to water vapor at all temperatures, and even ice evaporates. There is nothing magical about 100 C. $\endgroup$ May 5 at 11:16
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The key is the vapor pressure, which increases with increasing temperature and reaches 1 atm (760 mm Hg or torr) at 100°C:

This broadly corresponds to the broken molecular bonds that you refer to. Below 100°C, vapor bubbles, as the physical manifestation of the thermodynamic phase transition, simply can't resist the mechanical force of atmospheric pressure and therefore have a volume of zero. Above 100°C, vapor bubbles grow spontaneously, of course, as the effective internal pressure exceeds atmospheric pressure.

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If the heat energy countered the intermolecular forces, let say at $80^\circ$ celsius, then $80^\circ$ celsius would be considered as boiling point. At $100^\circ$ Celsius the heat energy is very strong so that it can break the intermolecular forces between the molecules.

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    $\begingroup$ I understood this but then why is the heat energy at 80 degree celsius present in the form of kinetic energy as the intermolecular force should overpower it and it should be in the form of potential energy (ie. no movement of the particles should be there ). $\endgroup$ May 5 at 5:46
  • $\begingroup$ @VEDANSHTYAGI No, since the heat energy is continuous (like boiling water on the stove), then intermolecular forces couldn't overcome the heat energy, as there is a continuous supply of heat energy. $\endgroup$ May 5 at 5:53
  • $\begingroup$ @VEDANSHTYAGI Here's an analogy: The molecules are bunch of masses connected to each other with springs. Temperature is the amplitude that the mass-spring system is oscillating at. If you keep adding energy, the temperature increases so the oscillations is larger and larger. But at some point, the springs stretch so much they snap. If you keep adding energy, the energy goes into snapping more springs instead of increasing in amplitude of oscillation so it boils but temperature does not increase. $\endgroup$
    – DKNguyen
    May 5 at 7:17
  • $\begingroup$ @DKNguyen this makes it clear but another question that pops up in my mind is that why is the same pattern seen during boiling as the springs had already snapped once during melting. $\endgroup$ May 5 at 10:10
  • $\begingroup$ @VEDANSHTYAGI The thing about analogies is they aren't perfect. Don't try to equate 1:1 in any analogy outside of what has been said. Molecules can be rigidly bonded (solid) or slide around each other. You can keep throwing in stuff to a mechanical analogy but it defeats the explanatory purpose if you added sliding joints and locking notches, etc. $\endgroup$
    – DKNguyen
    May 5 at 19:52

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