CDS Physics · Heat and Thermodynamics

Change of State and Gases

Latent heat and why evaporation cools, the triple point of water, what the ideal gas model assumes, and how the common thermodynamic processes are named.

All Heat and Thermodynamics notes

Why this matters

Five CDS questions from 2017 (II) to 2026 (I). Two turn on latent heat in daily life, one on the triple point of water, and two on how gases behave: the ideal gas and the Joule-Thomson process.

Concept 1 of 2: Latent heat, evaporation and the triple point

When ice melts or water boils, you keep heating but the thermometer does not move. The heat is being used to break the bonds that hold the particles together, not to make them move faster. This hidden heat is latent heat. Evaporation also needs latent heat, and it takes that heat from whatever the liquid is touching. That is why sweat drying on your skin cools you.

Definition

Heat and change of state:

Latent heat: heat taken in or given out during a change of state, at constant temperature. $Q = mL$ .
Latent heat of fusion of ice: about $3.34 \times 10^{5}$ J/kg. Latent heat of vaporisation of water: about $2.26 \times 10^{6}$ J/kg, nearly seven times larger.
Evaporation happens at any temperature, from the surface only, and cools what is left behind. It is faster with more surface area, more wind, higher temperature and drier air.
Cotton in summer: cotton soaks up sweat and spreads it thin, so the sweat evaporates fast and takes latent heat from the body.
Triple point of water: the one temperature and pressure at which ice, liquid water and water vapour exist together: 273.16 K and about 611 Pa (about 0.006 atmosphere).

Heat for a change of state

Q = m\,L

Qheat taken in or given out, in joules
mmass that changes state, in kg
Llatent heat of fusion or of vaporisation, in J/kg

Worked example

How much heat turns 0.2 kg of water already at 100 °C into steam at 100 °C? Take the latent heat of vaporisation of water as

2.26 \times 10^{6}

J/kg.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

CDS · 2019 · CDS (II) 2019 — General Knowledge · Q115Moderate

Example 1 · Heat and Thermodynamics · Change of State and Gases

People prefer to wear cotton clothes in summer season. This is due to the fact that cotton clothes are

Latent heat changes the state, not the temperature

During melting or boiling the temperature stays fixed until the whole mass has changed state. Use

Q = mL

for that stage and

Q = mc\,\Delta T

only for the stages where the temperature changes.

The triple point is 273.16 K, not 273.15 K or 0 K

Ice, water and vapour coexist at 273.16 K and about 611 Pa. The ice point at normal pressure is 273.15 K, a hundredth of a degree lower. Any option with 0 K or 373 K for the triple point is wrong.

Drill 2 more on latent heat, evaporation and the triple point

Concept 2 of 2: The ideal gas and thermodynamic processes

An ideal gas is a simple model of a real gas. Its molecules are tiny points that fly about at random, bump into each other and the walls, and do not pull on one another between collisions. They do not all move at the same speed: some are slow and some are fast. When a gas is squeezed, heated or allowed to expand, the change is named after the quantity that stays fixed.

Definition

What the ideal gas model assumes:

Molecules have negligible size and no forces act between them, so the gas has no potential energy of attraction.
Collisions are perfectly elastic.
Molecular speeds are spread over a range (the Maxwell distribution), so the molecules do not all have the same speed or kinetic energy.
The average kinetic energy depends only on the absolute temperature.

Processes are named by what stays constant:

Isothermal: temperature. Isobaric: pressure. Isochoric: volume. Adiabatic: no heat enters or leaves.
Isoenthalpic: enthalpy. The Joule-Thomson (throttling) expansion, a gas forced through a porous plug, keeps enthalpy constant and is used to cool gases to very low temperatures.

Process	What stays constant
Isothermal	Temperature
Isobaric	Pressure
Isochoric	Volume
Adiabatic	No heat flows in or out of the gas
Joule-Thomson throttling	Enthalpy (an isoenthalpic process)

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

CDS · 2019 · CDS (I) 2019 — General Knowledge · Q83Moderate

Example 2 · Heat and Thermodynamics · Change of State and Gases

For an ideal gas, which one of the following statements does not hold true?

Equal average energy does not mean equal speeds

At one temperature the molecules of a gas have one average kinetic energy, but individual molecules move at many different speeds. A statement that all the molecules move at the same speed is false even for an ideal gas.

Isochoric is volume, isobaric is pressure

Iso means 'equal'. Isobaric keeps the pressure (bar) fixed, isochoric keeps the volume fixed, isothermal keeps the temperature fixed. Match the root before choosing.

Drill 1 more on the ideal gas and thermodynamic processes

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (1)

Latent heat, evaporation and the triple point
Heat for a change of state
$Q = m\,L$

Reference tables (1)

The ideal gas and thermodynamic processes5 rows

Process	What stays constant
Isothermal	Temperature
Isobaric	Pressure
Isochoric	Volume
Adiabatic	No heat flows in or out of the gas
Joule-Thomson throttling	Enthalpy (an isoenthalpic process)

Watch out for (4)

Latent heat changes the state, not the temperature
→ Latent heat, evaporation and the triple point
The triple point is 273.16 K, not 273.15 K or 0 K
→ Latent heat, evaporation and the triple point
Equal average energy does not mean equal speeds
→ The ideal gas and thermodynamic processes
Isochoric is volume, isobaric is pressure
→ The ideal gas and thermodynamic processes

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