# Water Boiling Time Calculator

Is there a way to calculate out how quickly a body of water will boil? My primary concern is to measure in relationship to different temperatures. For example, heat at 100 degrees Fahrenheit versus 500 degrees Fahrenheit.

The amount of water and the container itself I am not concerned with, strictly some sort of equation I could use to get a measurement of time. Thank you!

• Your question is too vague to answer. Do you mean that you want to bring the water to boiling point, or turn it into steam? The answer will vary a great deal depending on the conditions and the power (not so much temperature) of the heater. – sammy gerbil Jun 22 '16 at 11:29

## 1 Answer

No, there is not because, contrary to your last sentence:

The amount of water and the container itself I am not concerned with, strictly some sort of equation I could use to get a measurement of time.

the boiling time is not a well defined quantity unless you take these things into account carefully. To calculate the rate of temperature rise you need to know the amount of water, the rate at which heat is input and the rate at which heat is lost from the body of water. The shape and makeup of the container both affect the last point radically. Experimentally, try boiling the same quantity of water on the same stove in the same pot with and without the lid on and time both cases. You'll almost certainly get a considerable speeding up of the process with the lid on.

For a given rate of heat input and a given mass of water, we can give a lower bound to the time needed to bring the water to the threshold of boiling. If we neglect heat loss (i.e. we assume we heat water in something like a calorimeter), then, at temperatures between room temperature and boiling point the water's specific heat capacity $\sigma$ is roughly constant. So if we have a mass $m$ of water and input heat at a rate of $P$ (say in joules per second = watts) then the rate of temperature rise will be $\dot{T} = P\,/\,(\sigma\,m)$. Therefore, the time $t$ needed to raise the temperature from ambient $T_a$ to boiling $T_b$ is defined by:

$$\frac{T_b-T_a}{t} = \frac{P}{\sigma\,m}$$