One watt sounds small beside the electrical rating of a compressor. At liquid-helium temperature, however, a continuous watt of heat reaching the liquid can represent a substantial evaporation duty. Translating that heat into a liquid equivalent helps buyers ask better questions about insulation, transfer lines and operating costs.
The useful result is not a universal prediction of tank losses. It is a calculation with a stated boundary: where the heat enters, the helium state, the duration and what happens to the vapour.
Start with the cold-end heat load
A watt is one joule per second. A steady 1 W reaching the helium over 24 hours supplies 86,400 J, or 86.4 kJ. This is thermal energy at the cold boundary, not 1 W of electrical input to a refrigerator. Heat intercepted by an intermediate shield is also not automatically heat reaching the liquid.
Define whether a quoted value covers the vessel alone, its neck and supports, or the complete installation including transfer connections and instruments. Our insulation guide distinguishes these heat paths; thermoacoustic oscillations can add a less obvious contribution.
A stated-property liquid-equivalent calculation
For this example, take saturated liquid helium at approximately 4.22 K and 1.013 bar absolute. Air Liquide's property table gives a latent heat of vaporization of 20.754 kJ/kg and liquid density of 124.74 kg/m³, or 0.12474 kg/L, at its listed boiling point. These are state-specific values, not constants for every helium pressure.
The latent-heat-equivalent mass is energy divided by latent heat. Divide that mass by liquid density to express it in liquid litres:
Liquid equivalent (L) = heat load (W) × time (s) ÷ [20,754 J/kg × 0.12474 kg/L].
| Heat reaching helium | Thermal energy | Liquid equivalent |
|---|---|---|
| 0.1 W | 8.64 kJ | 3.34 L |
| 0.5 W | 43.2 kJ | 16.69 L |
| 1.0 W | 86.4 kJ | 33.37 L |
The 1 W case corresponds to about 4.16 kg on this latent-heat basis. Figures are rounded arithmetic, not measurement accuracy or a specification for an SG Trading vessel. The calculation assumes a constant heat load and allocates it entirely to the stated phase-change duty; it excludes cooldown, pressure changes and other energy flows.
Liquid equivalent is not automatically helium lost
In a closed vessel before any discharge, total helium mass can remain unchanged while energy, pressure, temperature and the distribution between liquid and vapour change. A constant-pressure evaporation equivalent cannot predict that pressure rise or holding time. The historical NBS Monograph 111, Technology of Liquid Helium, discusses closed-vessel storage separately from transfer and evaporation.
Even in a rigid vessel held at constant saturation pressure, a falling liquid level creates more vapour space. Part of the helium remains there. Liquid depletion and mass leaving the vessel are therefore different accounting quantities. If vapour is collected for reuse, it has changed phase without necessarily being lost from the wider facility.
At other pressures, use corresponding properties and an appropriate energy balance. Jefferson Lab's helium property table illustrates how liquid density and vaporization energy vary with temperature along saturation. Do not extrapolate this reference-state calculation towards the critical point or use it for a two-phase transient calculation.
Translate the duty into a cost question
Suppose a proposed improvement reduces the cold-end heat load by 0.2 W for 30 days. At the example state, its latent-heat equivalent is approximately 200 L. This is an illustrative sensitivity calculation, not a promised saving.
If accepted operating evidence shows that this actually avoids purchasing 200 liquid litres on the same quantity basis, a marginal delivered price P per litre gives an avoided purchase cost of 200 × P. Where vapour was already recovered, the benefit may instead concern less purification or reliquefaction duty, more capacity, or improved availability. Count only the costs actually avoided; account separately for capital, maintenance and utilities.
Compare supplier figures on one basis
- Identify the thermal boundary and included components.
- State pressure as absolute or gauge, liquid state, fill condition and ambient conditions.
- Separate steady operation from initial cooldown and transfer events.
- Ask whether the figure is calculated, measured on a component or measured on the complete assembly.
- For percent-per-day figures, identify the inventory used as the denominator.
- Record vapour recovery, refrigeration, uncertainty and the test endpoint.
Use Gas Calc for its stated quantity and price conversions, and the helium-loss guide for the handover balance. Include the measurement basis in an RFQ rather than asking only for the lowest boil-off percentage.
Educational calculation, not a tank holding-time assessment, acceptance test or operating procedure. Do not change venting, relief protection or refrigeration settings to reproduce this example. Equipment-specific review belongs with qualified personnel and the approved documentation.