How much energy is required to keep water hot?

Question

I have a hot-water jug that keeps water hot (say, at about $70\, ^{\circ} C$). To compute its operation cost, I would like to compute its daily energy consumption. The label on the jug says "800 Watts", but this is probably the maximum power used when it is actively heating the water. I would like to know how much energy is spent, on average, to keep the water hot. Some more details:

• The room temperature is about $20\, ^{\circ}C$.
• The jug is made of steel plates with air between them (maybe there is another insulating material between the plates—I could not find out exactly).
• The jug capacity is about 5 litres, but usually it contains about 2 litres of water.

Based on this information, is it possible to approximate how much Watt*hour it consumes per day?

Answer 1

The simplest approach here is to neglect radiative losses (small at these low temperatures) and use Newton's Law of Cooling as a simple model:

$$\dot{Q_{loss}}=UA\left(T_w-T_{env}\right)$$

where:

• $T_w$ is the water temperature and $T_{env}$ is the ambient temperature
• $U$ is the overall heat transfer coefficient and $A$ the jug's surface area.

The estimation of $U$, depending on the jug wall's composition, can be found here.

The jug is made of steel plates with air between them (maybe there is another insulating material between the plates—I could not find out exactly)

In order to compute an estimate of $U$ the precise material dimensions and characteristics would have to be known.