IN30 · Heat under a peak

Differential Scanning Calorimeter

What do an endothermic peak’s area and position tell us? After blank and sensible-heat correction, a complete peak gives the heat absorbed per unit mass in a transition. Its position also depends on heat transfer and the speed of the transition. Faster heating can move the peak to a higher temperature while leaving the total absorbed heat nearly unchanged.

Heat a sample and empty reference together. Compare slow and fast scans, correct the blank and integrate the extra heat absorbed in a transition.

Drag the sample disc upwards to increase its mass. Save another scan after a change; the retained curves keep their original conditions.

Heating rate

10\,\mathrm{K\,min^{-1}}

Sample mass

10\,\mathrm{mg}

Assumed equilibrium transition

150\,{}^\circ\mathrm{C}

Transition enthalpy

80\,\mathrm{J\,g^{-1}}

Phase relaxation time

12\,\mathrm{s}

A complete thermal scan and independently checked references are loaded.

Heat capacity, endpoints and contact

Specific heat / joules per gram kelvin

1.2

Ramp endpoint / Celsius

180

Final hold / seconds

80

Thermal link / watts per kelvin

0.012

Random seed

20330

Voltage and thermometer noise

Changing the thermal link changes the physical post radius and invalidates the old sensitivity calibration. A new reference run restores a compatible record.

Model assumptions

One symmetric twin-pan heat-flux architecture is modelled. A finite-capacity furnace drives two thermal links; sample enthalpy contains constant sensible heat and one finite-width equilibrium step with first-order phase relaxation. Raw voltage, thermometer channels, setpoint and matched blanks are retained. Known heat-capacity and indium fusion references set sensitivity; independent temperature, heat-capacity and transition references check it. Enthalpy is conditional on constant sensible heat, calibrated sensitivity and a complete final tail. Peak temperature describes the scan and is separate from equilibrium transition temperature. Synthetic geometry, density, kinetics and sensor performance are teaching assumptions; heat markers, colours and faster replay are schematic. Reference, mass and hardware uncertainties are not fully propagated.

Retained simulated measurements

The area and the peak answer different questions

Saved scan

Conditional transition enthalpy

80.0\,\mathrm{J\,g^{-1}}

Apparent peak: sample temperature

150.84\,{}^\circ\mathrm{C}

Specific heat from the baseline

1.20\,\mathrm{J\,g^{-1}\,K^{-1}}

Largest sample temperature lag

2.28\,\mathrm{K}

Raw sensor, blank and calibration

Two reference baths calibrate each thermometer; a third is withheld. Known heat-capacity and indium-fusion references calibrate voltage-to-heat-flow sensitivity. Separate heat-capacity and transition runs check it. The reference with constant specific heat and both withheld materials are synthetic. Indium adopts the NIST 2024 central fusion values; its sensible heat and broadened kinetics are teaching assumptions.

Baseline, finite tails and interpretation

Ten percent of transition energy

149.59\,{}^\circ\mathrm{C}

Half of transition energy

150.92\,{}^\circ\mathrm{C}

Ninety percent of transition energy

155.68\,{}^\circ\mathrm{C}

Endothermic heat flow is positive. A matched empty-pan run removes a linear voltage baseline. Pre-transition energy between one hundred ten and one hundred twenty-five Celsius estimates constant specific heat. The integral also corrects the sensible energy stored in the two pans when their temperatures differ. Full enthalpy needs a settled final tail; a truncated scan retains its partial energy but withholds a complete transition result. Peak and energy-quantile temperatures describe this heating program, not an independently measured equilibrium melting point.

Readouts are conditional on the stated thermal network, matched blanks, measured mass and constant sensible heat. No complete metrological uncertainty interval is supplied: reference certification, mass, pan heat capacity and conductance uncertainties are not propagated. The resolution guard is a conservative signal threshold, not a confidence interval.

Architecture and schematic scale

One common furnace heats lumped pans through two equal, massless effective thermal links. The sample has one reversible finite-width equilibrium enthalpy step with first-order phase relaxation. The furnace has finite heat capacity, feedback control and ambient loss. Power compensation, modulated DSC, gradients inside a pan, reactions, evaporation, radiative exchange between cells and heat carried by leads are omitted. Geometry is in millimetres. Synthetic link conductivity sets post radius; a synthetic density of one point two grams per cubic centimetre converts mass into sample height. The indium preset adopts fusion values, not real indium geometry. Sensor view removes the pans to reveal their junctions. Heat markers, colours and accelerated replay are schematic.

Start with the essentials

Focus question: Why can the peak move while its integrated heat stays almost the same?
One-sentence intuition: The energy of a completed transition and the time at which that energy enters are different quantities.

Core mathematical model

Heat-flux difference

\dot Q_{\Delta}=G(T_r-T_s)

The two links have the same conductance. Positive signal means that more heat enters the sample-side assembly than the reference-side assembly.

The pan also stores sensible heat

\dot Q_{\Delta}=mc_p\dot T_s+m\Delta h\dot x+C_{\mathrm{pan}}(\dot T_s-\dot T_r)

The sample has constant specific heat and a phase fraction describing how much has transformed. The last term accounts for unequal temperature changes of the otherwise identical pans.

A completed transition from its time integral

m\Delta h=\int \dot Q_{\Delta}\,dt-mc_p\Delta T_s-C_{\mathrm{pan}}\Delta(T_s-T_r)

This gives full latent heat only when the phase change is complete. The blank-corrected voltage and thermometer observations supply every term.

Common difficulties

Temperature on the horizontal axis

Typical misconceptionArea under a heat-flow-versus-temperature plot is already an energy.

Better mental modelHeat flow is power. Temperature intervals must be converted to elapsed time using the actual heating history before energy is integrated.

Peak versus equilibrium

Typical misconceptionThe highest point of every heating peak is the equilibrium melting temperature.

Better mental modelFinite heat transfer and phase kinetics affect the peak. Temperature standards and an explicit onset convention are needed for a material-temperature claim.

Run the experiment

01
Change the real sample
Drag the sample disc upwards, then save a new scan.
What to observe: The increased height represents increased mass. Both sensible and latent energy demand grow, while earlier saved curves remain unchanged.
02
Scan slowly and quickly
Compare A slow scan and A fast scan shifts the peak.
What to observe: The apparent sample peak and half-energy temperatures move. With the complete tail retained, the integrated enthalpies remain close.
03
Inspect the actual temperatures
Compare the program, common furnace, reference and sample curves.
What to observe: A programmed temperature is not the temperature of every cell. Furnace response and sample relaxation produce separate delays.
04
Change the link
Open the contact settings, change Thermal link and save a scan.
What to observe: Old sensitivity is incompatible. Acquire new references to calibrate the changed physical posts before reporting a new enthalpy.
05
Stop too soon
Choose An unfinished tail.
What to observe: The retained curve contains partial transition energy. A complete enthalpy and normalized transition temperatures are withheld.
06
Follow the sensor
Open Thermopile junctions and inspect the raw sensor and blank panel.
What to observe: The pans are removed in this cutaway so both temperature junctions are visible. The signal is their difference, with a separately measured voltage baseline.

Differential Scanning Calorimeter

The area and the peak answer different questions

Heat enters two pans at different rates

Core mathematical model

Heat-flux difference

The pan also stores sensible heat

A completed transition from its time integral

Common difficulties

Temperature on the horizontal axis

Peak versus equilibrium

Run the experiment

Change the real sample

Scan slowly and quickly

Inspect the actual temperatures

Change the link

Stop too soon

Follow the sensor

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