Convert -40\ ^C to kelvin. [1 mark]

SingaporePhysicsSyllabus dot point

What does temperature actually measure, and what does it mean for two bodies to be in thermal equilibrium?

Define thermal equilibrium and thermodynamic temperature, relate the kelvin and Celsius scales, and explain temperature as a measure of average molecular kinetic energy

A focused answer to the H2 Physics learning outcome on temperature. Thermal equilibrium and the zeroth law, the thermodynamic (kelvin) scale, its link to Celsius, and temperature as a measure of average molecular kinetic energy.

Generated by Claude Opus 4.87 min answerUpdated 2026-06-06

Reviewed by: AI editorial process; not yet individually human-reviewed

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What this dot point is asking
The answer
Examples in context
Try this

What this dot point is asking

SEAB wants you to define thermal equilibrium and thermodynamic temperature, to convert between the kelvin and Celsius scales, and to interpret temperature microscopically as a measure of the average kinetic energy of molecules. These ideas frame the whole thermal physics section.

The answer

Thermal equilibrium

Two bodies in thermal contact are in thermal equilibrium when there is no net flow of thermal energy between them. This happens precisely when they are at the same temperature. Energy always flows from the hotter to the colder body until their temperatures equalise.

The zeroth law of thermodynamics formalises this: if A is in equilibrium with B, and B with C, then A is in equilibrium with C. This is what allows a thermometer (body B) to measure temperature reliably.

Thermodynamic temperature and the kelvin

The thermodynamic (absolute) temperature scale is measured in kelvin (K) and starts at absolute zero, the temperature at which a system has its minimum possible internal energy. There is no temperature below absolute zero.

The kelvin and Celsius scales have the same size of degree, related by:

T(\text{K}) = \theta(^\circ\text{C}) + 273.15

So $0\ ^\circ\text{C} = 273.15\ \text{K}$ and absolute zero is $-273.15\ ^\circ\text{C}$ . All gas laws and the kinetic theory require temperatures in kelvin, because only then is the average molecular kinetic energy proportional to temperature.

Temperature and average molecular kinetic energy

Microscopically, temperature is a measure of the average translational kinetic energy of the molecules of a substance. For an ideal gas:

\langle E_k \rangle = \tfrac{3}{2}kT

where $k$ is the Boltzmann constant and $T$ is the absolute temperature. A higher temperature means faster-moving molecules on average. At absolute zero the molecular kinetic energy is at its minimum.

Why kelvin, not Celsius, in equations

Because $\langle E_k \rangle \propto T$ only when $T$ is measured from absolute zero, doubling the kelvin temperature doubles the average molecular kinetic energy. Doubling the Celsius temperature does not, which is why physics equations always use kelvin.

Worked example

A hot metal block at $80\ ^\circ\text{C}$ is placed in contact with a cooler block at $20\ ^\circ\text{C}$ . (a) Convert both temperatures to kelvin. (b) Describe the energy transfer and final state.

Step 1: Convert to kelvin

$80\ ^\circ\text{C} = 80 + 273.15 = 353\ \text{K}$ (3 s.f.).

$20\ ^\circ\text{C} = 20 + 273.15 = 293\ \text{K}$ (3 s.f.).

Step 2: Identify the direction of energy flow

Thermal energy flows from the hotter block ( $353\ \text{K}$ ) to the cooler block ( $293\ \text{K}$ ), since energy always flows from high to low temperature.

Step 3: Describe the approach to equilibrium

As the hot block cools and the cool block warms, the temperature difference falls and the rate of transfer decreases.

Step 4: State the final state

The blocks reach a common temperature between $293\ \text{K}$ and $353\ \text{K}$ (its exact value depends on their masses and specific heat capacities). At that point they are in thermal equilibrium with no net energy flow.

Examples in context

Example 1. Why a metal handrail feels colder than a wooden one. Both are at the same room temperature and in thermal equilibrium with the air. The metal feels colder only because it conducts thermal energy away from your hand faster. This separates the ideas of temperature (equal here) from rate of energy transfer.

Example 2. Calibrating a thermometer. A thermometer reaches thermal equilibrium with whatever it touches, then reads that body's temperature. The zeroth law guarantees that a thermometer calibrated against one body will read correctly for any other body at the same temperature, which is what makes measurement meaningful.

Try this

Q1. State what is meant by absolute zero and its value in degrees Celsius. [2 marks]

Cue. The temperature of minimum internal energy, $0\ \text{K} = -273.15\ ^\circ\text{C}$ .

Q2. Convert $-40\ ^\circ\text{C}$ to kelvin. [1 mark]

Cue. $-40 + 273.15 = 233.15\ \text{K} \approx 233\ \text{K}$ .

Q3. Explain, in terms of molecular motion, what happens to the average kinetic energy of gas molecules when the temperature is raised from $300\ \text{K}$ to $600\ \text{K}$ . [2 marks]

Cue. Since $\langle E_k \rangle \propto T$ in kelvin, doubling the temperature doubles the average molecular kinetic energy, so the molecules move faster on average.

Exam-style practice questions

Practice questions written in the style of SEAB exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

Original4 marks(a) Explain what is meant by thermal equilibrium between two objects. (b) Convert

27\ ^\circ\text{C}

to kelvin and explain why the thermodynamic temperature scale starts at absolute zero.

Show worked answer →

(a) Two objects are in thermal equilibrium when they are at the same temperature, so there is no net flow of thermal energy between them when they are in contact.

(b) $T(\text{K}) = \theta(^\circ\text{C}) + 273.15$ , so $27\ ^\circ\text{C} = 27 + 273.15 = 300.15\ \text{K} \approx 300\ \text{K}$ .

The thermodynamic scale starts at absolute zero ( $0\ \text{K}$ ), the temperature at which a system has minimum internal energy (molecular motion is at its lowest possible). A scale measured from this natural zero makes quantities like average molecular kinetic energy directly proportional to temperature.

Markers reward defining equilibrium as equal temperature with no net heat flow, the correct conversion, and the meaning of absolute zero as minimum internal energy.

Original3 marksA thermometer placed in a beaker of hot water initially reads a rising temperature, then settles to a steady value. Explain this behaviour in terms of thermal equilibrium and energy transfer.

Show worked answer →

When first inserted, the thermometer is cooler than the water, so thermal energy flows from the water to the thermometer; its reading rises.

As the thermometer warms, the temperature difference shrinks and the rate of energy transfer falls.

When the thermometer reaches the same temperature as the water, they are in thermal equilibrium: there is no net energy flow, and the reading is steady at the water's temperature.

Markers reward energy flowing from hot to cold while a difference exists, the falling rate as the difference shrinks, and the steady reading at equilibrium when temperatures are equal.