--- title: "Differential Scanning Calorimeter Interactive Lab | Sandbox Physics" description: "What do an endothermic peak’s area and position tell us?" canonical_url: "https://sandboxphysics.com/labs/differential-scanning-calorimeter/" language: "en" page_type: "lab" alternate_languages: zh-CN: "https://sandboxphysics.com/zh/labs/differential-scanning-calorimeter/" last_modified: "2026-11-04" --- 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. > Interactive simulation: open this page in a web browser to change the parameters and run the model. 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 $2.28\,\mathrm{K}$ > Interactive plot; retained observations and model assumptions are described below. > Interactive plot; retained observations and model assumptions are described below. Raw sensor, blank and calibration > Interactive plot; retained observations and model assumptions are described below. 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. Physics tutorial ## Heat enters two pans at different rates **Background** A common furnace warms a sample and an empty reference pan through two thermal links. The sample needs sensible heat to warm, and extra heat during its transition. **Why it matters** The temperature difference is a sensor signal. Its conversion into heat flow needs calibration, a matched blank and the heat stored in the pans. 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 misconception** Area under a heat-flow-versus-temperature plot is already an energy. **Better mental model** Heat flow is power. Temperature intervals must be converted to elapsed time using the actual heating history before energy is integrated. #### Peak versus equilibrium **Typical misconception** The highest point of every heating peak is the equilibrium melting temperature. **Better mental model** Finite 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 1. 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. 2. 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. 3. 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. 4. 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. 5. 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. 6. 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. Physical conclusion Integrate calibrated excess heat over time, keep the entire tail, and identify peak temperature as a scan-dependent quantity. ## Related experiments and articles How physics instruments measure · Reading path ### How physics instruments measure Articles on this path that use this experiment, followed by the other experiments they suggest. 1. [Article **How Differential Scanning Calorimetry Reads a Melting Peak**](https://sandboxphysics.com/stories/instruments/differential-scanning-calorimeter/) Fields & matter · Starter path ## From a field to an electron microscope Map an electric field and steer a charged particle. Then find the electron's wavelength and use electron beams to see a crystal and a surface. [Start here → **Make an Electric Field Visible** Move the probe around a dipole and check that the field always points downhill on the potential landscape. 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