Physics · Thermodynamics

Temperature and Internal Energy

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Wrap-up

What you learned

Recommended next: Open concept testCheck whether the core ideas are ready without leaving this concept.
Read next: Ideal Gas Law and Kinetic TheoryConnect average particle motion to gas pressure.

Key takeaway

Temperature tracks average microscopic motion per particle, not the total energy in the whole sample.
Internal energy grows with both the amount of substance and the microscopic stores represented on the bench.
The same heater power can warm a smaller sample faster, while a phase shelf can absorb energy with little temperature change.

Common misconception

Equal temperature does not mean equal internal energy, and added energy does not guarantee an immediate temperature rise.

Equal temperature means the average kinetic energy per particle is similar.

Keep this idea moving

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Gas pressure bridgeThermodynamics

Ideal Gas Law and Kinetic Theory

Connect pressure, volume, temperature, and particle number on one bounded particle box, then read the same pressure changes back as changes in particle speed and wall-collision rate.

Where the energy goes nextThermodynamics

Heat Transfer

See heat as energy transfer driven by temperature difference while conduction, convection, and radiation compete on one compact bench with honest pathway rates.

How the energy changes TThermodynamics

Specific Heat and Phase Change

See why the same energy pulse changes different materials by different temperature amounts, and why a phase-change shelf can absorb or release energy without changing temperature on one compact thermal bench.

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Reference and support

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Equation snapshotAverage, amount, and input snapshot · Total thermal kinetic energyShow 3 equations

Keep the average-versus-total story visible: temperature follows average kinetic energy, while internal energy also depends on particle count and other microscopic stores.

Average, amount, and input snapshot
$K_{avg} = α T$
Temperature is represented here by the average thermal kinetic energy per particle.
Total thermal kinetic energy
$K_{thermal} = N K_{avg}$
The whole-sample thermal kinetic energy depends on both temperature and particle count.
Internal-energy bookkeeping
$U = K_{thermal} + U_{bond}$
Internal energy includes the thermal motion and the other microscopic stores represented on the bench.

Why it behaves this way

Explanation

On this particle bench, temperature tells you how energetic the particles are on average. Internal energy tells you how much microscopic energy the whole sample has altogether.

That is why amount matters. Two samples can show the same temperature and similar motion traces, yet the larger sample can still have more internal energy because that average motion is being counted across more particles.

When you heat the sample, watch both the stage and the graphs. Sometimes added energy raises temperature quickly, and sometimes it mainly fills another internal store, so internal energy rises while temperature changes little.

Key ideas

01Temperature tracks the average microscopic motion per particle, not the total energy of the whole sample.

02Internal energy depends on average motion, the amount of substance, and the other microscopic store shown on the bench.

03At the same heater power, a smaller sample warms faster because the same input energy is shared across fewer particles.

04On the phase shelf, energy can keep entering the sample even while the temperature graph stays nearly flat.

Worked examples

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Frozen walkthrough

Step through the frozen example

Frozen walkthrough

Use the current sample state as your evidence. The particle motion, energy bars, and graphs all come from the same live setup, so you can connect what you see on the stage to the numbers you calculate.

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Example 1 of 2

Frozen valuesUsing frozen parameters

For the current sample with $N = 12$ particles and temperature $2.8$ , use the live readouts to separate per-particle energy from whole-sample energy. What are the thermal kinetic energy and the total internal energy?

N

Particle count

T

Temperature

2.8 arb

K_{avg}

Average kinetic energy per particle

2.1 u

U_{bond}

Bond and phase store

10.8 u

1. Read the average per-particle energy

In this model, the current temperature corresponds to an average kinetic energy of

K_{avg} = 2.1 u

per particle.

2. Multiply by particle count

Multiply by the amount of substance:

K_{thermal} = N K_{avg} = 25.2 u

3. Add the other internal store

The current non-kinetic store is

U_{bond} = 10.8 u

, so the total internal energy is

U = 36 u

Thermal part and total internal energy

K_{thermal} = 25.2 u, U = 36 u

This smaller sample can still have the same temperature because temperature follows the average particle motion, not the total amount of energy stored across all particles.

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Thermodynamics and Kinetic Theory

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