---
title: "Thermogravimetric Analyzer Interactive Lab | Sandbox Physics"
description: "After heating, how do we separate real mass loss from buoyancy and drift? A matched empty-pan heating run reveals buoyancy and balance drift."
canonical_url: "https://sandboxphysics.com/labs/thermogravimetric-analyzer/"
language: "en"
page_type: "lab"
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  zh-CN: "https://sandboxphysics.com/zh/labs/thermogravimetric-analyzer/"
last_modified: "2026-11-04"
---

IN31 · A hot specimen on a balance

# Thermogravimetric Analyzer

**After heating, how do we separate real mass loss from buoyancy and drift?** A matched empty-pan heating run reveals buoyancy and balance drift. Subtract it, correct the specimen’s own displaced gas and compare the remaining loss across heating rates and atmospheres. The curve measures mass change; identifying evaporation or a chemical reaction needs additional evidence.

Heat a suspended specimen under flowing gas. Correct empty-pan readings and compare three heating rates to test a conditional single-step kinetic model.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

Base heating rate $\mathrm{K\,min^{-1}}$ $10$ Main standard gas flow $\mathrm{mL\,min^{-1}}$ $50$ Initial sample mass $\mathrm{mg}$ $10$ Main gas

A complete simulated record is loaded.

Hold the gold valve grip and rotate. Save a new record to compare the changed setup.

Reaction assumptions and program

Final setpoint $500$ Final hold / seconds $240$ Assumed releasable mass fraction $0.3$ Assumed activation / kilojoules per mole $110$ Assumed rate at 650 kelvin / per second $0.015$ Noise seed $20431$ Weighing and thermometer noise

The initial hold lasts sixty seconds. The base and twice-base ramps fit one model; half-base is withheld. All runs cool and recondition the balance to the same initial state.

Model assumptions

One hang-down, force-compensation thermobalance is modelled. A synthetic solid releases carbon dioxide in one first-order step. Product pressure inhibits its forward rate; reversal, cooling, oxygen combustion, multiple reactions and chemical identification are outside this model. Furnace, specimen, gas chamber and balance have finite response. Each saved scan includes raw balance and thermometer counts, setpoints, matched blanks, two training ramps and one withheld ramp. Independent known mass, temperature, response and inert-specimen observations check the calibration. Displaced volume is independently specified and held constant during reaction. A feed-gas buoyancy approximation is shown separately from the conditional kinetic mass curve. Geometry, thermal constants, rates, standard performance and density are teaching assumptions. Colours, flow markers and accelerated replay are schematic; no complete metrological uncertainty interval is supplied.

Retained simulated weighing

## How much left, and when?

Saved three-rate record

Initial corrected mass $10.0\,\mathrm{mg}$

Observed endpoint loss $30.0\,\%$

Fastest loss: actual sample $348\,{}^\circ\mathrm C$

Conditional activation energy $110\,\mathrm{kJ\,mol^{-1}}$

> Interactive weighing plot; the measurement and interpretation are explained below.

> Interactive derivative plot; units and assumptions appear below.

Temperatures, raw sensor and independent checks

> Interactive temperature channels.

> Interactive raw balance channels.

Two known cold masses calibrate gain and offset; a third mass is withheld. Two reference baths calibrate each thermometer; a third checks it. A known load step calibrates balance response and an independent step checks it. An empty-pan ramp estimates thermal and time drift; a separate inert specimen verifies the complete correction. All reference values and hardware dimensions are synthetic teaching definitions.

What the correction assumes

Upward buoyancy and gas drag reduce apparent mass. Matched blanks remove the pan and reproducible drift; the specimen’s own displaced volume needs a separate correction. The gold observed curve uses feed-gas density. Reaction products can alter chamber density, so the purple kinetic mass additionally depends on the fitted product-gas balance. Its activation energy assumes one first-order forward branch, known carbon dioxide inhibition and constant displaced volume. Two ramps fit the parameters; the slower third ramp never enters that fit.

A derivative peak is a scan-dependent rate maximum, not an equilibrium decomposition temperature or a chemical identifier. A single constant-temperature rate cannot separate activation energy from its prefactor. Missing final tails, unresolved loss, incompatible references and failed withheld predictions stop kinetic reporting. No complete uncertainty interval is supplied: reference, volume, mass, gas-law and thermal-model uncertainty are not fully propagated. The observed derivative includes balance lag and a twenty-second smoothing window.

Apparatus and schematic scale

Geometry is in millimetres. One pan hangs from a null-balance beam outside the furnace; an electromagnetic coil compensates its force and a capacitive sensor detects position. The mechanical null loop is idealized fast; the acquired current readback has its own finite response. A separate nitrogen purge protects the balance. The main gas crosses the pan and exits through the side port; arrows summarize a well-mixed two-cubic-centimetre chamber. The measured sample temperature is assumed representative of a lumped specimen. A synthetic initial density of one point five milligrams per cubic millimetre sets its volume, which stays fixed as mass escapes. Furnace and specimen store sensible heat; the declared reaction absorbs heat. Gas density follows an ideal-gas mixture, and flow modifies a declared effective heat conductance. Internal gradients, reverse reaction, multiple steps, turbulence, corrosion and evolved-gas spectroscopy are omitted. Hot colour and moving gas markers are schematic, not emitted light or resolved fluid trajectories.

Physics tutorial

## The balance feels the gas as well as the specimen

**Background** A suspended pan stays inside a heated gas chamber while a protected microbalance balances its downward force. Its coil current becomes a mass-equivalent sensor signal.

**Why it matters** Heating changes gas density and reaction speed together. An empty pan and independent standards distinguish those contributions before a kinetic model is fitted.

Start with the essentials

- **Focus question**: Why can the loss peak move even when the final lost mass is unchanged?
- **One-sentence intuition**: The mass of released material and the temperature at which it escapes describe different aspects of the same process.

### Core mathematical model

#### Apparent mass in a gas

$$
m_{\mathrm{app}}=m_{\mathrm{solid}}+m_{\mathrm{pan}}-\rho_gV+F_{\mathrm{drag}}/g+b(t,T_b)
$$

Buoyancy points upward. The gas density and displaced volume include the pan and suspension as well as the specimen; flow drag has its own sign.

#### Declared single-step model

$$
\dot\alpha=k_{650}\exp\!\left[-\frac{E}{R}\left(\frac1{T_s}-\frac1{650\,\mathrm K}\right)\right](1-\alpha)\max\!\left(0,1-\frac{p_{\mathrm{CO_2}}}{p_{\mathrm{eq}}(T_s)}\right)
$$

Absolute temperature enters the Arrhenius factor. This is a synthetic first-order forward branch with product inhibition, restricted to monotonic heating.

#### Loss derivative on a clock

$$
\mathrm{DTG}=-\frac{100}{m_0}\frac{dm}{dt}
$$

The displayed loss rate is percent per minute. Differentiation uses a twenty-second window and includes the finite balance response.

### Common difficulties

#### A derivative peak is not a species label

**Typical misconception** One peak identifies one chemical compound.

**Better mental model** Different evaporating or reacting materials can lose the same mass. Gas analysis or independent chemistry is needed to identify the escaping product.

#### One constant temperature

**Typical misconception** A single isothermal decay determines both activation energy and prefactor.

**Better mental model** It determines their combined rate at that temperature. Many parameter pairs share that rate; different heating histories help separate them.

### Run the experiment

1. 01

   #### Turn the gas valve

   Hold the gold grip and rotate it, then save the changed setup.

   **What to observe:** Flow changes gas residence time, heat transfer and force on the pan. Old records retain their original setup.

2. 02

   #### Replace the atmosphere

   Compare A complete loss with Product gas inhibits.

   **What to observe:** The product-rich gas delays the assumed release reaction. A narrow reaction-temperature range can leave the activation energy unresolved.

3. 03

   #### Heat quickly

   Choose Heating outruns the sample and inspect the temperature curves.

   **What to observe:** The programmed temperature, furnace and actual specimen separate. The fitted rate uses the measured specimen channel.

4. 04

   #### Inspect the blank

   Open the raw sensor and calibration panel.

   **What to observe:** Even an empty pan drifts during heating. Each specimen run has a separate blank under the same program, gas and flow.

5. 05

   #### Stop early

   Choose The tail is missing.

   **What to observe:** The observed partial loss remains visible. Full-step normalization and activation parameters are withheld.

Physical conclusion

Keep time, actual specimen temperature, raw weighing and matched blanks together. Test a conditional kinetic fit on a heating rate excluded from that fit.

## 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 thermogravimetry separates mass loss from the gas around it**](https://sandboxphysics.com/stories/instruments/thermogravimetric-analyzer/)

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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. Observe · 8 min](https://sandboxphysics.com/labs/electric-field/)

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