Drop a fistful of ice cubes into a pan, sit it on a low flame, and push a thermometer into the slush. Now watch the reading. The ice-and-water mixture climbs to 0 °C and then — strangely — stops. The flame is still roaring, energy is still pouring in, minute after minute, and yet the thermometer refuses to budge past 0 °C until the very last shard of ice has melted. Only then does the temperature start to rise again.

So where is all that energy going while the reading sits frozen at 0 °C? It isn't lost, and it isn't making anything hotter. It is being spent changing the state of the water — prising the solid ice apart into liquid — without changing its temperature at all. The energy a substance secretly swallows to melt or boil (or gives back when it freezes or condenses) is called its latent heat, and it is the one idea on this page. "Latent" means hidden: heat that goes in, but doesn't show up on the thermometer.

The energy hiding in a change of state

To melt a solid or boil a liquid, its tiny bits must be dragged out of the tight grip they hold on one another. That takes energy — a lot of it — and while it is happening every joule goes into breaking bonds, not into speeding the bits up. Since temperature is really just "how fast the bits are jiggling," the temperature holds dead still throughout the change.

The specific latent heat of a substance — symbol L — is the energy needed to change the state of 1 kilogram of it, with no change in temperature. Its unit is therefore \text{J/kg} (joules for each kilogram). To find the energy for a real lump of stuff, scale L up by how much stuff there is — the mass m in kilograms:

For water, melting one kilogram of ice needs about 334{,}000\ \text{J}, so its specific latent heat of melting is L = 334{,}000\ \text{J/kg}. Boiling one kilogram of water into steam needs a colossal 2{,}260{,}000\ \text{J} — nearly seven times more, as we'll see next.

Two kinds: fusion and vaporisation

There are two different changes of state, so each substance has two specific latent heats:

• The specific latent heat of fusion (L_f) is for the solid ⇄ liquid change — melting going in, freezing coming back. You add this energy to melt; you get exactly the same amount back when it freezes. For water, L_f \approx 334{,}000\ \text{J/kg}.
• The specific latent heat of vaporisation (L_v) is for the liquid ⇄ gas change — boiling going in, condensing coming back. For water, L_v \approx 2{,}260{,}000\ \text{J/kg}.

Notice the huge gap: vaporisation needs far more energy than fusion — for water about 2{,}260{,}000 / 334{,}000 \approx 6.8 times as much. Melting only has to loosen the bits so they slither past each other; boiling has to rip them completely apart and fling them out into a gas, with no grip on their neighbours at all. That is a far bigger job, so it drinks far more energy.

Reading it off a heating curve

Heat a block of ice steadily and plot its temperature against time. The line does not just rise in a straight ramp — it climbs, then goes flat, then climbs, then goes flat again, then climbs. Each flat plateau is a change of state: the energy is still arriving at a steady rate, but it is all going into breaking bonds, so the temperature parks itself while the whole kilogram melts (at 0 °C) or boils (at 100 °C). The rising stretches are where specific heat capacity rules — energy raising the temperature — and the flat stretches are where latent heat rules.

Drag the mass slider. Everything stretches sideways, because more mass means more energy for every step — and the live readout shows E = m\,L for melting and boiling. Watch how the boiling plateau is far wider than the melting plateau: that width is vaporisation's much larger latent heat, drawn to scale.

Worked example 1 — melting ice

How much energy is needed to melt 3\ \text{kg} of ice at 0 °C into water at 0 °C? (For water, L_f = 334{,}000\ \text{J/kg}.)

Step 1 — pick the right latent heat. This is melting, so use the latent heat of fusion, L_f = 334{,}000.

Step 2 — put the numbers into E = m\,L.

Step 3 — multiply.

Just over a million joules — and notice the thermometer never moves off 0 °C for the whole process. Every one of those joules went into turning solid into liquid, not into making anything hotter.

Worked example 2 — how much can we boil? (rearranging for m)

A kettle element delivers 1{,}130{,}000\ \text{J} of energy into water that is already boiling at 100 °C. What mass of water does it turn to steam? (L_v = 2{,}260{,}000\ \text{J/kg}.)

Step 1 — rearrange E = m\,L to make m the subject:

Step 2 — substitute and work it out.

So over a million joules boils away just half a kilogram of water — a good reminder of how thirsty vaporisation is. It is also why a pan of water takes an age to boil dry once it reaches 100 °C: the temperature is stuck, and all that energy is quietly being swallowed as latent heat.

Worked example 3 — measuring a latent heat (rearranging for L)

In the lab, an immersion heater pours 40{,}800\ \text{J} into a beaker of melting ice and melts 0.12\ \text{kg} of it. What is the specific latent heat of fusion this experiment measures?

Step 1 — rearrange for L:

Step 2 — put the numbers in.

That is very close to water's true value of 334{,}000\ \text{J/kg} — the small excess is energy that leaked in from the warm room melting a little extra ice, which is exactly why the real experiment is insulated. This is precisely how latent heats are measured: count the energy in, weigh the mass that changed state, and divide.

Latent heat vs specific heat capacity

These two ideas are easy to muddle, so line them up side by side. They are the two things heat can do to a substance:

• Specific heat capacity (\Delta E = m\,c\,\Delta\theta) governs the rising stretches of the heating curve — energy that changes the temperature while the state stays the same.
• Specific latent heat (E = m\,L) governs the flat stretches — energy that changes the state while the temperature stays the same.

One moves the thermometer; the other moves the substance between solid, liquid and gas. To heat a block of ice at −20 °C all the way to steam you need both in turn: warm the ice (mc\Delta\theta), melt it (mL_f), warm the water (mc\Delta\theta), boil it (mL_v), then warm the steam (mc\Delta\theta) — a rise, a flat, a rise, a flat, a rise.

Where the idea shows up

Latent heat isn't a lab curiosity — it's why a steam burn is so vicious and why sweating keeps you alive on a hot day. Both are the very same physics, running in opposite directions.