Heat a beaker of ice steadily and plot temperature against time. The graph is not a ramp — it is a staircase of slopes and plateaus, and each kind of segment has its own machine. On a slope the temperature climbs and $Q = mc\,\Delta T$ answers. On a plateau the thermometer sits still while energy pours in, and the machine is $Q = mL$ — Q equals m L, where $Q$ is the heat in joules, $m$ is the mass changing phase in grams, and $L$ is the specific latent heat in joules per gram: the price of changing one gram's phase, with no temperature change bought at all.

Water carries two of them: melting costs $L_f = 334\ \mathrm{J/g}$ (the subscript f is for fusion, the chemist's word for melting) and boiling costs $L_v = 2260\ \mathrm{J/g}$ (v for vaporization). Nearly seven times as much — which is why a pot takes minutes to reach boiling and then a quarter of an hour to boil dry. The named exam wound: reaching for $mc\,\Delta T$ on a plateau. There $\Delta T = 0$, so the machine cheerfully reports that melting an iceberg is free. Look at which segment the question lives on BEFORE you pick up a formula.