A temperature logger gives these (time in min, temperature in °C) pairs: (0, 64), (2, 54), (4, 50), (6, 50), (8, 44). The sample may change state near 50 °C; its mass was constant. Calculate the signed mean temperature-change rates over 0–2 min and 6–8 min. Test the claim that temperature changed at a constant rate throughout. Explain what the record can and cannot reveal about energy transfer, and propose one follow-up measurement.

Question

Accepted Answer

First rate -5 °C/min; last rate -3 °C/min. The sampled intervals do not support a constant temperature-change rate throughout. Temperature alone is insufficient to determine transferred energy. Use change divided by elapsed time, preserving the sign: (54 − 64)/2 = -5 °C/min over the first interval. A negative value means cooling, not a negative temperature. For the last interval the equivalent calculation is (44 − 50)/2 = -3 °C/min. Compare equal-duration intervals rather than comparing their final temperatures alone. Check every successive change: -5, -2, 0, -3 °C/min. They are not all equal, so one straight-line rate cannot describe the complete record. Interpret the stated conditions before claiming a mechanism: The sample may change state near 50 °C; its mass was constant. A plateau can accompany energy transfer during a state change, and a local probe reading need not equal the whole sample's temperature. Temperature is not itself an energy measurement. Record sample mass and material properties, check probe calibration and repeat with room temperature logged; if a state change is possible, observe the phase as well. This separates a thermal explanation from changing experimental conditions.

Cooling through a change of state

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Recorded sample temperature

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Recorded sample temperature — supplied values
Time (min)	Temperature (°C)
0	64
2	54
4	50
6	50
8	44