Adiabatic Expansion: Cooling Without Losing Heat

1 · Predict

A gas expands quickly, with no time to exchange heat with its surroundings (adiabatic). Does the gas's temperature change even though no heat enters or leaves?

• The gas cools down — it does work on its surroundings using its own internal energy.
• The temperature stays the same, since no heat is exchanged.
• The gas heats up as it expands.

2 · Set Up

1. Open the adiabatic-expansion preset and press Reset. 1 mol of diatomic nitrogen (f = 5) starts at 0.0249 m³, 300 K.
2. Enable the final-temperature readout on the chamber.
3. Set the target (final) volume for each trial, and record the final temperature and the work done.

3 · Collect Data

Plot final temperature T₂ (y-axis) against final volume V₂ (x-axis) for your three trials. Does the line curve downward?

4 · Analyze

1. For one trial, compute T₂ = T₁·(V₁/V₂)^(γ−1) using γ = (f+2)/f = 1.4, T₁ = 300 K, V₁ = 0.0249 m³. Then compute W_gas = −ΔU = −(f/2)nR(T₂ − T₁). Compare both to the table.
2. With Q = 0 in every trial, the first law gives ΔU = −W_gas exactly. Explain, in terms of energy conservation, why an expanding gas that does positive work must cool down when it can't draw in heat.

5 · Extend

1. An aerosol spray can feels cold as gas rushes out and expands rapidly — too fast to exchange much heat with the surroundings. Explain why this is a real-world (if imperfect) example of adiabatic cooling.
2. Compare your final temperatures here to what isothermal-compression's reverse (an isothermal expansion) would give for the same volume change: isothermal keeps T constant, but this adiabatic case doesn't. Why does removing the heat-exchange assumption change the outcome?

The Physics Behind This Experiment

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