Heat a pot of ice and watch the thermometer. It climbs to 0 °C, then STOPS while the ice melts, then climbs again to 100 °C, then stops again while the water boils. Those flat stretches are not the kettle resting. They are the most expensive parts of the whole journey.

$Q = mL$ — Q equals m L. $Q$ is the heat in kilojoules, $m$ is the mass changing phase in kilograms, and $L$ is the specific latent heat in kJ/kg: what one kilogram costs to change phase, at constant temperature. Latent means hidden — hidden from the thermometer, because the energy goes into pulling molecules apart rather than into making them jiggle faster. There is no $\Delta T$ in this relation, and that absence is the entire point.

Water carries two of them, and mixing them up is the named mistake of this lesson. $L_f$, the latent heat of fusion, is 334 kJ/kg: melting ice, or freezing water. $L_v$, the latent heat of vaporisation, is 2257 kJ/kg at atmospheric pressure: boiling water, or condensing steam. The subscripts name the phase change, not an order of events.

Put those beside sensible heat and the scale of it lands. Melting a kilogram of ice costs about the same as warming that kilogram of water by eighty degrees. Boiling it costs nearly seven times more again. A steam plant is built the way it is because of that second number: steam carries a colossal amount of energy per kilogram, and hands every joule of it back the moment it condenses on something cold.