Question

When baking, cooking or writing recipes, it would be useful to have a ballpark estimate of evaporation rates. This question asks about water, although the answer would ideally include an interchangeable variable to account for other substances, such as cooking oils.

Essentially, I would like to build a calculator program that I could just type in these variables, and be able to answer the following questions:

How much water will evaporate after 10 minutes of boiling?
How long will it take for my 500 grams of water to boil down to 300 grams?
There are some other questions on StackExchange which kind of ask similar questions, but the scope is too broad. For example, there is no wind in an indoor kitchen, so we would be able to use an established value for wind activity. Another example: we know there's negligible solar radiation in a kitchen that doesn't meaningfully change the equation. There's also multiple citations referencing one particular webpage, The Engineering ToolBox. However, that website and its javascript calculator seems to account for large bodies of water (such as swimming pools) and it's unclear how to scale it down into something useful for a kitchen.

Basically, in a kitchen, there are known variables:

The substance (water)
The initial mass of the substance (500 grams)
The initial temperature of the substance (23°C)
The evaporative surface area in centimetres (1/4πd², where is the diameter of your saucepan, 16 cm → 201 cm²)
The air temperature (23°C)
The air humidity percentage (65%)
Some more complicated, yet still accessible variables are:

The kitchen's position above sea level (therefore, the air pressure)
The cooking medium's heat capacity (stainless steel, copper, cast iron)
The heat output of your stove, in BTUs or joules (induction, electric, gas)
Perhaps, though this is speculative, the theoretical equation would be simpler if it assumed the saucepan and water begins at boiling temperature (100°C, perhaps?).

Surely, using these variables, there must be an equation that can be used to determine the mass of water evaporation over time, when cooking. Does anybody know how to do this?

Answer 1

The rate of evaporation of water can be determined using the latent heat of vaporization and the rate of energy supply. Other factors such as surface area, air temperature, and humidity can also be considered to obtain a more accurate estimate.

Step-by-step explanation:

The rate of evaporation of water, and other substances, can be determined using the heat energy required for evaporation. The heat energy required for evaporation is known as the latent heat of vaporization. In the case of water, it takes 2,250 J of energy to evaporate each gram of water. To calculate the amount of water that will evaporate over a specific time period, you will need to know the rate at which energy is being supplied to the system and the time duration.

For example, if it takes 10 minutes to bring a pot of water from room temperature to boiling, and the rate of energy supply remains constant, the additional time it will take to evaporate all the water can be calculated by dividing the total heat energy required to evaporate the water by the rate of energy supply.