Water Heating Calculator

Our water heating calculator can help you determine both the amount of heat required to raise the temperature of some H₂O and the time it will take. It considers the heat capacities of all three states of matter, so it also works if you want to melt the ice or boil water.

If you're wondering what's the limit of how hot water can get, what is the heat capacity, and how it all relates to your water heater BTU (British Thermal Unit) - read on!

This question may sound trivial, but is it really? Yes and no. Although it seems obvious to think of a kettle, stove, boiler, or another device, all of them are just tools that we use to change the temperature more easily.

To heat water, you need to... well, add heat, which is one of the forms of energy. Doing so increases the average kinetic energy of the molecules and hence also the directly proportional temperature, as stated in the kinetic theory. There are three types of heat transfer:

• Conduction occurs when two objects are in contact. There's a certain heat flow from the hot object to the cooler via molecule agitation (collision of high-speed particles with the slower ones). Some substances are better conductors than others, so we're usually interested in the material's thermal conductivity. An example of this type of transfer would be a pan on the stove or holding an ice cube in your hand.

• Convection applies to fluids (including air!). When the liquid's temperature increases, it becomes less dense and rises. At the same time, the cooler counterparts will move downwards, creating convection currents. They are circular movements that help spread the heat throughout the substance. It explains, for example, why the ocean water is warmer on the surface than if you swim deeper.

• Radiation, on the contrary, doesn't need molecules as it happens via electromagnetic waves. It means that no medium nor physical contact is required. All objects emit and absorb radiation, some more than others. Stefan-Boltzmann Law tells us how much power is radiated from a body at a certain temperature. This is how Earth gets the heat from the Sun.

All of these methods of heat transfer apply to our case, but it's unlikely that you're going to consider radiation for everyday purposes. Nevertheless, the method doesn't impact the amount of heat required to raise the temperature, so our water heating calculator will help you even in a more unusual setting.

Talking about heat may be confusing. There are a few terms that sound similar but mean completely different things. However, they're all critical to understanding how to calculate the energy needed to heat water, so we've gathered all of them with an explanation:

• Heat, as we've mentioned, is one of the forms of energy that's transferred because of temperature differences. Therefore, its units are, typically, Joules (J).

• Specific heat capacity is a property of the material defined as the amount of heat required to raise the temperature of 1 kilogram of a substance by 1 Kelvin (or Celsius, since the scale is the same in terms of increments - an increase of 1 K is equal to an increase of 1 °C). It follows that its units are J/kg⋅K or J/(kg⋅°C). The British thermal unit (BTU) is defined similarly but talks about raising the temperature of a pound of H₂O by 1 degree Fahrenheit. Hopefully, you see how the water heater BTU is related to this now!

• Latent heat, on the contrary, doesn't refer to a change in temperature but a phase. This is the amount of heat required to turn, e.g., a liquid of some mass into a gas - you could think of what happens to water at 100 °C when it becomes steam. In this case, the units are J/kg.

Although sporadically considered, it's worth knowing that the value of latent heat changes with the pressure, whereas the specific heat varies depending on the temperature. The water heating calculator uses the most standard values of these constants.

The amount of energy you'll need to change the temperature of the water depends on its initial and final states. Generally, you need to consider two quantities:

1. Heat required to raise the temperature, $Q_t$:

where:

• $c$ is the specific heat capacity;
• $m$ is the mass;
• $T_f$ is the final temperature; and
• $T_i$ is the initial temperature.

This quantity is also known as sensible heat.

2. Heat needed to change the phase, $Q_\mathrm{p}$:

where:

• $L$ is the latent heat. If there's a transition from ice to water, we're considering the latent heat of fusion, whereas for the phase change from a liquid into steam, it's the latent heat of vaporization.

Finally, all you need to do is sum up all heat values to calculate the energy needed to heat H₂O. For just one phase, you'll have a single number, but otherwise, there's going to be more. Luckily, our water heating calculator takes care of it for you!

If you know the efficiency and the power of the heater, you can also compute the time required to reach the final temperature. The formula is:

where:

• $Q_{\text{total}}$ is the total energy found earlier.

If you can measure the input and output energy, the efficiency calculator can also help.

How much energy would you need to obtain water hot enough to brew some tea from a 1 kg block of ice with an initial temperature of -10 °C (263.15 K)? We can break it into smaller steps:

1. Calculate the heat needed to raise the temperature of ice until 0 °C:

   $Q_{\text{ice}} = 1 \ \text{kg} \times 10 \ \text{K} \times 2,\!108 \ \frac{\text{J}}{\text{kg} \cdot \text{K}} = 21,\!080 \ \text{J.}$

2. Find the amount of heat required to convert it into the water:

   $Q_{\text{ice} \to \text{water}} = 1 \ \text{kg} \times 334,\!000 \ \frac{\text{J}}{\text{kg}} = 334,\!000 \ \text{J.}$

3. Determine how much energy you need to heat the water. Let's assume that the perfect temperature would be 96°C (369.15 K):

   $Q_{\text{water}} = 1 \ \text{kg} \times 96 \ \text{K} \times 4,\!190 \ \frac{\text{J}}{\text{kg} \cdot \text{K}} = 402,\!240 \ \text{J.}$

4. Sum up all the values to get the total energy needed:

   $Q_{\text{total}} = 21,\!080 + 334,\!000 + 402,\!240 = 757,\!320 \ \text{J.}$

5. An average kettle has 1800 Watts (W) of power. Assuming 90% efficiency, we can see that:

   $\text{time} = \frac{757,320 \ \text{J}}{0.9 \times 1,800 \ \text{W}} = 467.48 \ \text{s} \approx 7 \ \text{min}$

As you've probably noticed, this calculation may be a bit laborious and take almost as long as melting a block of ice. Perhaps it's a better idea to use the water heating calculator and get to work right away then!