How a Thermos Works
Heat can only travel in three ways: conduction through solid materials, convection through fluids, and radiation as electromagnetic waves. A vacuum flask systematically defeats all three — which is why a thermos can keep coffee hot for 12 hours.
The Three Modes of Heat Transfer
In thermodynamics, heat always flows from a hotter region to a cooler one — never the reverse (Second Law). But the route it takes depends on the medium:
Mode 1 — Conduction
When you hold a metal spoon in hot soup, the heat travels along the spoon to your fingers. This is conduction: lattice vibrations and (in metals) free electrons carry thermal energy through solid matter.
Fourier's Law of heat conduction gives the rate of heat flow:
Thermal conductivity k varies enormously across materials:
| Material | k (W/m·K) | Relative conductivity |
|---|---|---|
| Silver | 429 | Extremely high |
| Copper | 401 | Very high |
| Glass | 1.0 | Low |
| Air (still) | 0.025 | Very low |
| Vacuum | ≈ 0 | Essentially zero |
| Aerogel | 0.015 | Lowest solid known |
A vacuum has essentially zero thermal conductivity because there are no atoms to vibrate and carry energy. A thermos flask has a vacuum gap between two glass (or steel) walls — typically about 1 mm wide at pressures below 0.001 Pa (≈10⁻⁵ atmospheres).
Mode 2 — Convection
Convection moves heat by bulk movement of fluid. When hot air or water rises (because it's less dense), cooler fluid replaces it, creating a convective current that efficiently redistributes thermal energy.
The rate of convective heat transfer is described by Newton's Law of Cooling:
The convection coefficient h for a hot mug in still air is about 5–25 W/m²·K — enough to cool coffee noticeably in minutes. By removing the air from the gap between the flask walls, a thermos eliminates convective heat loss entirely. No fluid, no convection.
Mode 3 — Radiation
Unlike conduction and convection, radiation does not require any medium. Every object with a temperature above absolute zero emits electromagnetic radiation — predominantly infrared at everyday temperatures. This energy travels at the speed of light through vacuum.
The total power radiated per unit area is given by the Stefan–Boltzmann Law:
Because radiation scales with T⁴, small temperature differences create large radiative fluxes. A mug at 80°C (353 K) radiates significantly more than its surroundings at 20°C (293 K).
Crucially, a vacuum cannot stop radiation — this is how the Sun's energy reaches Earth. To block radiation, the thermos uses a different trick.
How a Vacuum Flask Beats All Three
Sir James Dewar invented the vacuum flask in 1892 for storing liquid nitrogen and hydrogen. The design is elegantly simple:
- Double-walled construction: Two concentric glass (or stainless steel) cylinders.
- Vacuum gap: The air is evacuated from the space between the walls — blocks conduction and convection.
- Silvered walls: Both inner surfaces are coated with a thin layer of silver — reflects radiation back.
- Thin support: The two walls are connected only at the narrow neck — minimising the conduction pathway.
- Insulating stopper: The cork or plastic lid prevents convection at the opening.
| Heat transfer mode | Thermos countermeasure | Effectiveness |
|---|---|---|
| Conduction (walls) | Vacuum gap between walls | ~99% blocked |
| Convection | Vacuum gap (no gas to convect) | 100% blocked |
| Radiation | Silvered walls reflect IR | ~95–99% reduced |
| Conduction (neck) | Narrow glass/steel neck only | Partially reduced |
| Convection (top) | Insulating lid/stopper | Significantly reduced |
Stefan–Boltzmann Law: Why Silver Matters
The emissivity ε determines how efficiently a surface radiates (and absorbs) infrared. A perfect black body has ε = 1. Polished silver has ε ≈ 0.02 — it radiates (and absorbs) only 2% as much as a black body at the same temperature.
This means a silvered wall reflects about 98% of incoming infrared radiation. The net radiative heat transfer between the two silvered walls of a thermos is dramatically reduced:
Real-World Performance Numbers
A typical quality vacuum flask loses heat at roughly 0.5–2°C per hour for a hot liquid, compared to 5–15°C per hour for a ceramic mug in still air. The remaining heat loss is almost entirely through:
- The neck: Both walls must physically connect somewhere — the glass/steel at the narrow neck conducts heat around the vacuum.
- Residual gas: Even at 0.001 Pa there are still some gas molecules conducting at a very slow rate.
- Radiation: Even with silver coating, the ~2% that penetrates adds up over 12 hours.
- The stopper: Every time you open the flask, warm air escapes and cold air enters.
Beyond the Thermos
Vacuum insulation principles appear in many engineering contexts:
- Cryogenics: Liquid nitrogen (−196°C) and liquid helium (−269°C) are stored in large Dewar flasks using the same multi-layer vacuum insulation.
- Spacecraft: The James Webb Space Telescope uses a five-layer sunshield made of aluminised Kapton — each layer reflects radiation and the gaps act like vacuums (since space is a vacuum already).
- Vacuum-insulated panels (VIPs): Used in refrigerator walls, they achieve k ≈ 0.005 W/m·K — 5× better than the best foam — allowing thinner walls for same insulation.
- Double-pane windows: The argon gas between panes reduces convection (argon has lower k than air); some triple-pane windows use a partial vacuum.
- Space suits: Astronaut suits use multiple reflective layers and vacuum gaps to manage the extreme temperature swings in orbit (−150°C in shadow, +120°C in full sunlight).
Try It Yourself
Explore heat conduction and molecular dynamics — the microscopic origin of thermal conductivity — in the simulation:
See how the atmosphere traps radiated heat from the Earth's surface — the same Stefan–Boltzmann radiation at work on a planetary scale: