Latent heat — phase transitions — Physics notes

WHAT is latent heat?

Notice $L_v \gg L_f$ for water — WHY? Boiling pulls molecules completely apart against intermolecular attraction (and pushes back the atmosphere), whereas melting only loosens a rigid lattice into a still-touching liquid. Far more energy is needed for total separation.

WHY does temperature stay constant during a phase change?

This is the deepest "WHY" of the subtopic: heat energy splits into kinetic (→ temperature) and potential (→ phase). During a phase transition it is all potential.

HOW to read a heating curve (derivation of total heat)

When you steadily heat a block of ice from below $0°C$ to steam above $100°C$ , you cross 5 regions. The total heat is just the sum:

$Q_{\text{total}} = \underbrace{m c_{\text{ice}}\,\Delta T}_{\text{warm ice}} + \underbrace{mL_f}_{\text{melt}} + \underbrace{m c_{\text{water}}\,\Delta T}_{\text{warm water}} + \underbrace{mL_v}_{\text{boil}} + \underbrace{m c_{\text{steam}}\,\Delta T}_{\text{warm steam}}$

Why this form? Sloped regions (temperature rising) use $Q=mc\,\Delta T$ ; flat plateaus (phase change, $\Delta T=0$ ) use $Q=mL$ . Each region is independent — energy simply adds.

Figure — Latent heat — phase transitions

Worked Example 1 — melting ice

Q: How much heat melts $200$ g of ice already at $0°C$ ? ( $L_f = 3.34\times10^5$ J/kg)

$Q = mL_f = 0.200 \times 3.34\times10^5 = 6.68\times10^4 \text{ J} \approx 66.8\text{ kJ}$

Why this step? The ice is already at $0°C$ , so no $mc\Delta T$ term — every joule goes straight into fusion.

Worked Example 2 — full heating curve

Q: Heat $50$ g of ice at $-10°C$ to steam at $110°C$ . Data: $c_{\text{ice}}=2100$ , $c_{\text{water}}=4186$ , $c_{\text{steam}}=2010$ J/kg·K; $L_f=3.34\times10^5$ , $L_v=22.6\times10^5$ J/kg. $m=0.05$ kg.

Step	Formula	Value (J)	Why
Warm ice $-10\to0$	$mc_{\text{ice}}(10)$	$1050$	sloped, $\Delta T=10$
Melt at $0°C$	$mL_f$	$16700$	plateau, $\Delta T=0$
Warm water $0\to100$	$mc_{w}(100)$	$20930$	sloped, $\Delta T=100$
Boil at $100°C$	$mL_v$	$113000$	plateau, $\Delta T=0$
Warm steam $100\to110$	$mc_{s}(10)$	$1005$	sloped, $\Delta T=10$

$Q_{\text{total}} = 1050+16700+20930+113000+1005 \approx 1.527\times10^5\text{ J}$

Why this step? We split the journey at each kink in the curve; the boiling plateau dominates (113 kJ) because $L_v$ is huge.

Worked Example 3 — calorimetry (mixing)

Q: $300$ g water at $25°C$ is cooled by dropping in ice at $0°C$ . How much ice fully melts if the water cools to $0°C$ ? ( $L_f=3.34\times10^5$ , $c_w=4186$ )

Heat released by water: $Q = m c_w \Delta T = 0.300 \times 4186 \times 25 = 31395\text{ J}$ This melts ice: $m_{\text{ice}} = \frac{Q}{L_f} = \frac{31395}{3.34\times10^5} \approx 0.094\text{ kg} = 94\text{ g}$

Why this step? Energy conservation: heat lost by water = heat gained (latent) by ice. The water gives up $mc\Delta T$ ; the ice "spends" it as $mL_f$ .

Common mistake Steel-manned common errors

1. "Adding heat always raises temperature." Why it feels right: In everyday life heating = getting hotter. Fix: During a phase change all heat becomes potential energy (bond-breaking), so $T$ stays flat. Look for the plateau!

2. Using $Q=mc\Delta T$ during melting/boiling. Why it feels right: It's the formula you used a second earlier. Fix: $\Delta T=0$ there → it would give $Q=0$ , absurd. Switch to $Q=mL$ on plateaus.

3. Forgetting to warm the liquid between fusion and vaporisation. Why it feels right: You think "ice → water → steam, two L terms." Fix: Water must still climb $0\to100°C$ — that's a separate $mc\Delta T$ slope.

4. Mixing up $L_f$ and $L_v$ . Fix: Vaporisation rips molecules fully apart → $L_v$ is much larger.

Recall Feynman: explain to a 12-year-old

Imagine a crowd of kids holding hands in a frozen huddle (ice). To get them to let go and wander (liquid) you have to give them energy — but while they're busy letting go, none of that energy makes them run faster, so the "temperature" stays the same. Only after everyone's free does new energy make them run quicker. To make them fly off in all directions (steam) you need a HUGE push to fully break apart — that's why boiling takes so much more energy than melting.

Flashcards

What does "latent" mean and why is the heat called that?

Latin for hidden; the heat is absorbed/released without any temperature change, so it's "hidden" from a thermometer.

State the latent heat equation with units.

Q=mL

, where

Q

in J,

m

in kg,

L

in J/kg.

Why does temperature stay constant during a phase change?

All added heat becomes potential energy (breaking intermolecular bonds), not kinetic energy, so average KE — and hence temperature — is unchanged.

Why is

L_v

much larger than

L_f

for water?

Vaporisation fully separates molecules against attraction (and does work on the atmosphere); fusion only loosens a lattice into a touching liquid.

Which formula on a flat plateau, which on a slope?

Plateau (ΔT=0):

Q=mL

. Slope (T changes):

Q=mc\Delta T

Approx value of

L_f

and

L_v

for water?

L_f\approx3.34\times10^5

J/kg,

L_v\approx22.6\times10^5

J/kg.

Heat to melt 200 g ice at 0°C?

Q=0.2\times3.34\times10^5=66.8

kJ.

In a heating curve, what physically corresponds to the two flat regions?

Melting (fusion plateau at 0°C) and boiling (vaporisation plateau at 100°C for water at 1 atm).

Connections

Specific heat capacity — the $Q=mc\Delta T$ partner used on the sloped regions.
Calorimetry — method of mixtures — energy conservation for mixing problems.
Kinetic theory of gases — explains KE↔temperature link behind constant- $T$ plateaus.
Evaporation vs boiling — surface vaporisation also uses latent heat (cooling effect).
First law of thermodynamics — $L_v$ includes internal-energy rise + work done pushing back the atmosphere.
Phase diagrams — where these transitions live in $P$ – $T$ space.

Concept Map

Hinglish (regional understanding)

Intuition Hinglish mein samjho

Dekho, jab tum ice ko heat dete ho aur woh $0°C$ par pahunch jaati hai, tab ek interesting cheez hoti hai: temperature ruk jaata hai, badhta hi nahi, jab tak saari ice melt nahi ho jaati. Yeh jo heat tum de rahe ho woh "gayab" nahi ho rahi — woh molecules ke beech ke bonds todne mein lag rahi hai. Isi chhupi hui heat ko latent heat kehte hain (latent matlab hidden). Formula simple hai: $Q = mL$ , jahan $L$ specific latent heat hai.

Ab WHY temperature constant rehta hai? Temperature actually molecules ki average kinetic energy ko measure karta hai. Phase change ke time saari heat potential energy ban jaati hai (bonds todne mein), kinetic energy nahi badhti, isliye temperature flat rehta hai. Jaise hi phase change complete, dobara temperature chadhne lagta hai. Yahi reason hai heating curve mein do flat plateaus dikhte hain — melting par aur boiling par.

Problem solve karte time ek hi galti sabse zyada hoti hai: log plateau par bhi $Q=mc\Delta T$ laga dete hain. Yaad rakho — slope par $mc\Delta T$ , flat par $mL$ . Aur water ke liye $L_v$ ( $22.6\times10^5$ ) bahut bada hai $L_f$ ( $3.34\times10^5$ ) se, kyunki boiling mein molecules poori tarah alag hote hain, melting mein sirf lattice dheela hota hai. Calorimetry problems mein bas energy conservation lagao: jo heat paani chhodta hai, wahi ice latent form mein leta hai. Bas itna pakka kar lo, latent heat ka pura chapter aasaan ho jaayega.

Latent heat — phase transitions

WHAT is latent heat?

WHY does temperature stay constant during a phase change?

HOW to read a heating curve (derivation of total heat)

Worked Example 1 — melting ice

Worked Example 2 — full heating curve

Worked Example 3 — calorimetry (mixing)

Flashcards

Connections

Concept Map

Hinglish (regional understanding)

Go deeper — visual, from zero

Test yourself — Thermodynamics

Connections