# How can 30 ml of water be heated in less than 10 seconds?

How is it possible to heat a tiny amount (30 ml)[1] of water to a high enough temperature to make a coffee, in less than 10 seconds and possibly instantly?

Most heaters that I know of heat water in no less than 90 seconds (induction heater) or 3 minutes which is way too much for my purposes, and a microwave oven takes me one minute and a half to heat.

[1] A single coffee is between 20 - 30 ml and my coffee machine makes 30 ml for each cup.

• Good espresso machines do this all the time - a hot heater block with enough thermal mass does just fine. – Jon Custer Feb 17 '15 at 18:22
• Thermal conductivity of water would make this not just a function of energy, but also surface area. Too thick and the bottom boils before the top gets up to temperature. Too thin and it will overshoot your desired temperature too fast to get it off the heating element. – Schwern Feb 17 '15 at 20:23
• Troops in Vietnam used tiny amounts of C4 explosive to make coffee in the field. It produced enough energy to heat a cupful extremely fast. pomakis.tripod.com/clips/clip23.html - I presume/hope it's not something you have lying around at home, or even in a lab, however. – Bob Tway Feb 18 '15 at 11:31
• 10 seconds or less, or it's free! WHAM!! The law of conservation of energy says it isn't free. – corsiKa Feb 18 '15 at 16:00
• @MattThrower Good to clarify they didn't blow up their coffee with the C4, they burnt the C4. C4 burns great and is extremely stable. Just don't run an electric charge through it. And if you have some C4, you probably have better things to do with it. On second thought, if you're a civilian with C4 the best thing (for the rest of us) you can do is burn it to heat your coffee. – Schwern Feb 18 '15 at 18:14

Well, let's do some math:

Assuming 30 mL of water is 30 g, and we want to heat our water from 20 °C to 90 °C, the energy required is: \begin{align}E&=C_Pm\Delta K \\ &=\left(4.18 \mathrm{\frac{ J}{gK}}\right)(30\mathrm{\ g})(70\mathrm{\ K})\\ &=8.778\mathrm{\ kJ}\end{align}

So how much power do we need to do this in a given time? "Instant" doesn't really mean anything, so let's go with 10 seconds:

\begin{align}P&=\frac{E}{t}\\ &=\frac{8778\mathrm{\ J}}{10\mathrm{\ s}}\\ &=877.8 \mathrm{\ W}\end{align}

This is not an enormous amount of power, but the trick is that it all has to go into heating the water. A good microwave outputs a fair bit more power than this, but it generally doesn't all get absorbed by such a such a small amount of water in only 10 seconds. Your best bet is probably an electric heating element directly inserted into the liquid, though I don't know if you can get a ~1000 W one small enough to sit in that much water.

As Jon Custer notes, it's not necessary to produce all the heat at once. If you heat some kind of thermal reservoir and flow the liquid past/through it, it reduces the demands on your heat source.

Edit: Also, I just tried this with a 1200 W microwave and it only took 15 seconds. How fast do you really need this coffee?

• "How fast do you really need this coffee?" Is this a trick question? – Williham Totland Feb 17 '15 at 20:57
• I really don't know which answer to select as best answer as all are great answers and explain many things in different ways. I'll go for the most voted one. About the microwave; I think I have a less powerful and old one. Well, now that I think of it, something in the range of 15-30 seconds is still great for UX. Thank you everyone, hope the answers will help other people like it did for me. – Alper Turan Feb 18 '15 at 9:19
• If this is an engineering challenge (i.e. your company manufactures espresso makers), the microwave solution is doable. 30 ml of water will absorb 900W of microwave energy without problems if you can engineer the geometry of the water reservoir and the placement of the microwave tube. A standard microwave oven cannot be optimized like that, and probably is tuned more for a plate of food. – MSalters Feb 18 '15 at 10:57
• Please bear in mind that heating water using microwaves is an extremely hazardous activity. Bad steam burns are common when water is heated this way due to pockets of superheated water. Related to this is the fact that microwaves do not heat water evenly due to their very nature (~3cm wavelength). – Stephen Feb 19 '15 at 6:19
• @Stephen: 12 centimeters, actually. And since 30 cl is about 3x3x3 cm, a well-designed solution can have a fairly constant heating across the whole container. Also, the dielectric constant of water shifts, so you can tune the system for 293K. Hotter water will then absorb less energy, which means the colder pockets are preferentially heated. – MSalters Feb 19 '15 at 11:47

As can be seen in the above graph, there is a local heat flux maximum for heating water, when the hot surface contacting the water is 30 degrees C above the boiling point, that is 130 degrees C at atmospheric pressure.

So to minimize time to boiling, contact a 130 degree C surface made of high thermal conductivity material (such as silver, copper or aluminum) with the water.

With heat flux over 100,000 Watts/m^2, you just need to make the surface area of contact large enough to acheive any desired heating time.

• (877.8 W) / (100,000 W/m^(2)) = 87.78 cm^(2). 30 mL / 87.78 cm^(2) = 3.4mm water depth (if on a flat plate). – user253751 Feb 18 '15 at 8:22

If you want the practical answer, get an instant hot water dispenser. Practical, HA! Ok, let's do some science!

First, what kind of coffee? At 30 ml I'm guessing you're making espresso. I'm going to go with 92C as the optimal temperature.

Second, I'm going to take your full 10 seconds. The rest of the process of making espresso takes far more time so whether it's 5 or 10 or 15 seconds doesn't make a real difference to how fast you get your morning hit.

Other answers have pointed out the amount of energy needed to bring your 30 ml up from room temperature, but you can make life easier on yourself and do what a lot of "instant boil" systems do and preheat. This allows you to use less energy (for the 10 seconds anyway) and bring the water up to temperature slower. This gives you a wider tolerance between the water being too cold and it being boiled away. If your water is already at 50 C that will only require about 500 W.

To deal with thermal conductivity, a wider surface area in contact with the heating element would serve to heat the water more quickly and more evenly. If the water is too thin, it can overheat before it is removed from the element. Too thick and the bottom may boil before the top reaches temperature.

We need a broad, flat surface that can output at least 500 W and that we can quickly add and remove small amounts of water from. Sounds like you need an electric skillet! A very clean one. Or the precision laboratory version. Buy one that can heat quickly and evenly.

Knowing when to remove the water is a problem. Measuring the temperature of 30 ml of water on a hot electric skillet is problematic. I would suggest trial and error with various skillet settings, times and initial water temperatures. You can do a lot of experimental rounds in 10 seconds. This would also allow you to include the cooling effect of whatever vessel you're transferring it into.

According to Michael Dryden's answer, it takes 877.8W to heat 30ml of water by 70C (from 20C to 90C)in 10s.

My electric shower is about 10 times that power (lets call it 8.778kW for convenience.) I don't like to shower at 90C. I am more than happy if my shower heats the water about half that temperature difference, say 35C (from 5C to 40C). So I would set it to deliver 300ml x 2 = 600ml every 10 seconds. That's 3.6L/minute, so my 5 minute shower uses 18L of water. Of course, if I did choose to raise the temperature by 70C in the shower, I would have to restrict it down to 300ml every 10 seconds, making it a continuous version of your experiment, scaled up by a factor of 10.

The last time I took a shower apart, the element was inside a copper vessel of about 300ml volume. So, if you restricted the flow to 300ml in ten seconds, your residence time in the element vessel would be... ten seconds!

As noted by Schwern, your issue isn't heating it, it's being able to control the temperature accurately. One method that hasn't been mentioned is dunking a calibrated lump of hot metal into it (or pouring it into a hot metal container.) But so far the best method is Michael Dryden's idea of using a microwave.

In industry, batch processes are only used for slow processes like brewing beer. Fast processes (such as those used in oil refining: cracking, reforming, alkylation, etc.) are done continuously. For economic reasons these processes are carried out as fast as possible in the smallest possible equipment, and continuous process is therefore the only practical way of doing them.

If you really need to heat water that rapidly, and the reactants consumed in your experiment are cheap, I suggest you set your experiment up as a continuous process, with a flow of water through it. That way you will be able to control the temperature accurately with an electric heater. A shower will probably be too powerful - try scaling everything down to something like a 25W soldering iron element (make sure it's sealed and 12V DC for safety!)

You can supply your equipment with water from a reservoir at the top and control the flow / residence time with a valve at the outlet at the bottom. If you want to try the same conditions with double the residence time, simply reduce both the water flow and the heater output to 50%.

You may optionally replenish the reservoir with tap water to the point of (near) overflow if you need to mix things into it.

When I did a conversion course from chemistry to chemical engineering, several of the practicals were set up like this. It's definitely the way to go if you want to study fast processes whether they be mixing, reaction kinetics, or whatever.

Regarding Dave's points about critical heat flux, the important thing is to make sure you have sufficient surface area for the volume being heated. I don't see it as a huge issue at your scale though. For 1kW, you need 100cm2 of heating surface for a flux of 100,000W/m2. Many newer kettles provide this (with heating over the whole bottom surface for a neater design) but older models with curly heating elements are above 100,000W/m2, approaching critical heat flux. These electric kettles 'roar' as they come to the boil due to cavitation.

If your reagents are delicate, though, you will need to space your heaters very narrowly, or even use steam injection. I remember one particularly nasty case of electric heaters converting an aqueous polymer solution into volatile aldehydes.

• Your shower does not have an output of 8.778kW. Standard electricity cables melt with that amount of power, consumer welding equipment is around 2.5kW. Your shower is not going to beat welding equipment (that would be one hell of a shower). – Mast Feb 19 '15 at 8:58
• @Mast: In Europe, a 230V/25A cable is quite common and delivers 5.7 kW. For electric heating, 380V/35A is also available which pushes you well over 13kW. But even in the US, the need to power 10kW+ air conditioners means that high-power supplies are available. – MSalters Feb 19 '15 at 11:51
• @Mast Any bathroom continuous-flow water heater needs that rating, or more (cf. amazon.de/b?node=2077608031), like 24kW/100+ Amps. They typically have their own dedicated wiring right to the fuse box, with their own fuse. Oh, and when the landlord decides to install it in an existing apartment building they must renew the house's rising mains as well. – Peter - Reinstate Monica Feb 19 '15 at 11:56
• @Mast besides Peter's one from Germany, here's one from the UK where 8.5kW is the lowest power available: screwfix.com/c/bathrooms-kitchens/showers/cat820272 As Peter says, it needs to be wired in permanently on its own circuit because it's too much current for a wall plug. Regarding welding equipment: Don't underestimate the heat capacity of water. Haven't you ever seen a blacksmith put a large metal object in water to quench it? it cools down pretty quick! I don't know what the rules are in USA, but instant electric showers are rare in Spain because the installed kW is too low – Level River St Feb 19 '15 at 13:44
• @Mast it all depends on local regs. UK homes have 100A main property fuse installed as standard. My Spanish property on the other hand has only 20A for the whole aparment, because in Spain you pay a premium for any more capacity. As a result, Spanish properties have either instantaneous gas heating, or a storage tank heater of about 50-100L capacity with a 1-2.4kW element (with a plug on it.) – Level River St Feb 19 '15 at 13:51

As others have shown the energy requirement is quite reasonable, the problem is delivering it to the water in that timeframe.

I would think a workable approach could be done with a collection of plates with very narrow spaces between them that can hold your 30ml. Make the plates out of something that's not too good a conductor. Feed an extreme current through the plates (very low voltage, though--you'll have a big step-down transformer) and it will get hot quickly. You'll have to figure the energy left in the plates and add it to the amount of power you are dumping through this.

Careful, a second run before the plates have cooled will certainly result in boiling water.

• Small problem: your plates supposedly are somewhat-decent electrical conductors. Metal, graphite, etc. Those have lots of free electrons which can conduct electricity, but also heat. So your proposed material is in fact not a thermal insulator. – MSalters Feb 19 '15 at 11:55
• @MSalters Who said anything about an insulator? – Loren Pechtel Feb 20 '15 at 4:25
• "Not too good a conductor" is an isolator. – MSalters Feb 20 '15 at 8:04
• @MSalters I mean something with enough resistance to use as a heating element, not something that's an insulator. – Loren Pechtel Feb 20 '15 at 22:41
• In that case, why not use the standard solution - a metal wire coil? The resistance there is obtained by it being thin and long. You want that here, because that length gives you a large surface. – MSalters Feb 20 '15 at 23:23

You could try Induction cooktops. 10 seconds for 30 ml should be enough at 700w or more, if you are using a flat and wide vessel (not all utensils are induction compatible).

# How to get instant coffee

There are already some good answers on how you could reasonably get a cup of coffee-temperature water within 10 seconds. However, what if you wanted to get it even quicker than that?

## Realistic solution: Use a boiler

If you already have hot water, you won't need to wait for 10 seconds before your cup is ready to go. This may not be the most economical solution to get your morning dose, but if you have a coffee shop and really need to churn out cups during peak times it may be interesting to look into this.

## Interesting solution: Use more power

If you don't like the idea of keeping your water hot all the time, you need something to heat it quickly. Of course you could use a huge heating element, but I suppose that it may be even quicker to use something like an explosion. You just need to make sure that no deadly chemicals end up in your cup.

Other answers already indicated that the main problem with using more power, is that it is hard to control the temperature. However, this should be solved with the following steps:

1. (Over) Heat some water
2. Measure the temperature (only needed if step 1 cannot produce a fixed temperature reliably)
3. Mix the right amount of this water/steam with cold water to get a cup ful of water at the desired temperature

Of course it will never be truely instant, but I imagine that you could get it done in a fraction of a second.

• Another solution that maybe is not so great for everyday use but very fast, is to enclose water in a metal container, and around it another enclosing where Calcium Chloride [CaCl2] is mixed with water [H2O] (note: not the same water needed to be heated!!) => Ca2+ (aq) + 2Cl-(aq) + Q which should heat the water in less than 10 seconds. – Alper Turan Feb 19 '15 at 17:38

You can easily add $3.9~\mathrm{g}$ steam to $26.1~\mathrm{ml}$ water of $20\mathrm{°C}$ to get $30~\mathrm{ml}$ water of $100\mathrm{°C}$ in less than ten seconds.

• Yeah. This is the power of direct steam injection. :o – aventurin Jun 6 '16 at 19:40

We need a wide, level surface that could result at the very least 500 W and that we can quickly include and get rid of small amounts of water from. Sounds like you require an good electric skillet! A very clean one. Or the precision laboratory version. Get one that could heat rapidly and also uniformly.