Topic 6 of 6
Cooling curves
A cooling curve records temperature against time. Read each interval by asking which state is present and how energy is leaving.
Net heating transfers energy from a hotter region to a cooler one. Temperature falls within a state, but can remain constant during a change of state at the stated conditions.
Interpret a liquid that cools and solidifies
The following supplied model readings describe an unspecified pure substance at fixed pressure. It starts as a liquid, and its solidification temperature is 50°C. Energy continues to leave the sample throughout. These are idealised values, not readings collected from an experiment.
Energy leaves during the solidification plateau
Supplied idealised readings for an unspecified pure substance at fixed pressure. The sample starts as a liquid. These readings illustrate interpretation; they were not collected from an experiment.
| Time / min | Temperature / °C |
|---|---|
| 0 | 80 |
| 1 | 65 |
| 2 | 50 |
| 3 | 50 |
| 4 | 50 |
| 5 | 35 |
| 6 | 20 |
0-2 min: the liquid cools from 80 to 50 °C.
2-4 min: liquid changes to solid at 50 °C. During solidification, both states are present.
4-6 min: the solid cools from 50 to 20 °C.
On the plateau, average particle kinetic energy stays unchanged while the interaction potential energy decreases. Internal energy falls as energy continues to leave the sample.
During the sloping intervals, temperature and average random particle kinetic energy decrease. During solidification, the amount of solid increases while the amount of liquid decreases. Energy still leaves, but the particle potential-energy contribution decreases while average random kinetic energy stays unchanged.
Worked interpretation
What can be said at 3 min?
The point lies within the solidification interval. Both liquid and solid are present, the temperature is 50°C, and energy is still being transferred out.
The reading does not show that half the sample is solid simply because 3 min is halfway between 2 and 4 min. That fraction would need additional information about the energy-transfer rate and the energy required for the whole transition.
Sketch from the physical stages
- Label both axes and units: temperature on the vertical axis, elapsed time on the horizontal axis.
- Start in the given state: for this liquid, draw a falling temperature towards 50°C.
- Mark the transition: draw the constant-temperature interval at 50°C and label it liquid plus solid. Continued energy loss makes more solid.
- Continue after the transition: once the sample is all solid, draw a falling temperature again.
If plotting readings, place their actual values first. If sketching without numerical data, do not invent an exact duration or make both sloping regions equally steep unless the information supports it.
A cooling gas can similarly condense at its condensation temperature for the stated pressure before the liquid cools further. Identify the specified transition; not every horizontal part is melting, and a cooling curve need not contain every possible state change.
Use a temperature probe and data logger
A probe and data logger can record temperature automatically at selected time intervals. The probe measures the temperature of its sensing region, not heat, latent heat or the whole sample's internal energy directly.
- Place the sensor: keep its sensing region in good thermal contact with the sample and clear of the vessel's base and walls. Maintain suitable contact as the sample changes state.
- Choose the range and interval: the probe must cover the sample's temperatures. Select a sampling interval short enough to show the transition, and keep the same time origin.
- Record and inspect: retain time units and temperature units, and observe the sample's state where possible. The graph must represent the recorded points, including any scatter.
- Evaluate the response: a slow sensor can round off changes in slope. Recording more often does not make the sensor respond faster.
In the model above, readings only at 1 min and 5 min would miss the entire 2 to 4 min plateau. More frequent sampling can reveal the interval, but cannot fix poor contact or an unsuitable response time.
Real cooling rates may change as the temperature difference from the surroundings changes. A fixed reading from a disconnected or poorly placed sensor is not evidence of solidification. Check the sensor and the observed state before assigning a physical explanation to a flat trace.
A flat temperature is not a flat energy account. During the stated solidification interval, internal energy decreases even though temperature stays constant.