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Specific heat is usually defined as the amount of energy that must be added to change the temperature. Another way to define it is the ratio between the amount of energy added and the change in temperature E/m·T(with units like joules/gram·°C) When water is at the saturation point and energy is added to it, instead of increasing in temperature, the water changes phase from liquid to gas. If you put the numbers back into the definition you get something like:

1 joule added to 1 gram of water yields a change of 0 °C so

Cp = 1/1∙0 = ∞.

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