What is the definition of latent heat and how does it apply to phase changes?

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I need some clarifications on the precise definitions and scope of latent heat. My textbook defines latent heat as the amount of energy absorbed or releases during a phase change process. So if I have a pot of liquid water and I vaporize it completely, then the latent heat is simply the energy I had to put into the system to completely vaporize the water? What if I only vaporize half of the liquid water? Would the latent heat be the energy I had to put into the system in order for that to happen or does latent heat not apply to this situation because not all of the water is vaporized?
 
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Latent Heat is the amount of energy needed to change the state of a substance without changing it's temperature. That's the concept. The quantity is usually defined to be the amount of heat needed to change the state of a standard reference mass of the substance since it clearly takes more heat to change the state of more substance.

eg. - the latent heat of vaporizaton for water is 2257kJ/kg ... i.e. you need 2257kJ to vaporize 1kg of water at 100degC (at std pressure). If you vaporized half a kg, that would need 1123.5kJ or half as much.

If you supplied 2.257kW of heat to the water, then it would take 1000s to vaporize 1kg of water.