# Heating water in a pot from a constant heat source

What are the equations used to calculate the amount of energy transferred from a constant heat source "like a stove" to a pot which would then transferred energy to water contained in that pot.

I don't know exactly what equation to ask about and just need some direction to go in for formulas.

To calculate the amount of heat energy needed to heat a pot with its content of water we can use a simple formula:

$$\Delta H=mc_p(T_2-T_1)$$

Where $\Delta H$ is the heat energy needed to heat an object of mass $m$ and specific heat capacity $c_p$ from $T_1$ to $T_2$. For a pot with water these energies would need to be calculated for both separately and then added. Here we assume the $c_p$ values to be temperature invariant, which tends to be true for reasonable temperature intervals.

But:

to calculate the amount of energy transferred from a constant heat source "like a stove"

...is much harder. Specifically when using a stove, burner or such like because the heat transfer from heat source to pot plus water tends to be quite inefficient: only part of the heat supplied by the heat source actually ends up in the pot plus kettle. The rest escapes as air heat, light and IR radiation.

If we call $\epsilon$ the percentage that gets lost, then the heat that must be provided by the heat source would be:

$$\Delta H_{source}=\frac{mc_p(T_2-T_1)}{100-\epsilon}\times 100$$

• Estimating efficiency should be challenging. It would probably be easier to actually measure efficiency by noting the power produced by the heater and the heat absorbed by the pot and water. Otherwise, you would have to worry about thermal conductivity, heat transfer coefficients, forced and natural convection, etc., etc. – David White Jul 24 '16 at 23:06
• @DavidWhite: absolutely. Estimating "$\epsilon$" ab initio would be a nightmare. – Gert Jul 24 '16 at 23:14