# Do you need a “smart” mug, or rather ordinary, or how fast the coffee cools

Gadgets enter our life firmly and inevitably. Some immediately find their niche, some need time for it. And there are those who are trying to impose sly marketers. Coffee is one of the pillars of IT. Not surprisingly, marketing has gone beyond coffee grades and types of coffee machines.

Here, for example, an article about a mug to maintain the temperature. It seems to be a good idea: to set the desired temperature from a smartphone, and enjoy the drink for an unlimited time (and in fact quite a limited one) But the phrase caught me
it is estimated that a comfortable temperature is maintained only 37 seconds
True, it is not clear by whom it was calculated and how. And at first glance it looks somewhat implausible. But subjective disbelief cannot be an argument. Let's figure it out.

There is a review of available materials and their own measurements.

## Some theory

The author indicates a “comfortable temperature” of 60-55º. In general, this is a problem for Newton's law of cooling:

The solution is:



$T\left(t\right)={T}_{0}+\left({T}_{s}-{T}_{0}\right){e}^{-kt};$

Where ${T}_{s}$$T_ {s}$- ambient temperature, and ${T}_{0}$$T_ {0}$- the initial temperature of the object, k - thermal conductivity coefficient.

Cooling rate, respectively:



Thus, the cooling rate is directly proportional to the temperature difference between the object and the environment. That is, the maximum cooling rate will be immediately after preparation (95º, the difference is 70-75º) and at 60º the difference with the environment will be only 35-40º. Not so much. And in order for the coffee to cool to 55º in 37 seconds, the cooling rate should be 8º / min.

Unfortunately, k in this formula depends on the circle itself, and can only be calculated empirically. True, a search on the Internet gives out quite a lot of practical work on measuring the rate of cooling of a cup of water. For example, a work very close in purpose. And here is its result:

That is, in a normal glass, the cooling rate is 1.2 degrees per minute at 60º. So to talk about 37 seconds, for which the water cools down to 0.74 º - this is purely a marketing ploy. When the “comfort temperature” declared by the author is 60-55º, the cooling time will be more than 4 minutes.

But such a result (1.2 ° C / min) seemed to me too optimistic. So I decided to raise my old experiments, where I compared the rate of cooling of tea and coffee.

## Measurements

To measure the temperature, a DS18B20 sensor was used (the manufacturer indicates accuracy of 0.5 º in the range of -10 + 85, the sensor is entered into the State Register of measuring instruments) and a USB-UART adapter on the FT232 (podoytet any USB-UART).

There are many programs that work with 1-wire via RS-232. Most of them accept the virtual com port. I used my program, because at that time I needed more than 2 sensors, and free programs or demo versions did not allow this.
We will compare the usual ceramic mug and the nameless thermo mug.

Mugs for testing

Water is poured in the same way to measure, although the capacity of the thermomug is greater.

Cooling schedule.

Cooling is shown from one point, although when pouring liquid, the initial temperature was different for different mugs. The target range for us is 60-55º. The cooling time of the closed thermomug from the moment of preparation of the drink to the “comfortable” temperature is almost an hour. Without a cap - about 20 minutes. And here the “smart” circle would be useful. If any of her characteristics were given. And then, if it cools the coffee the same half an hour, why is it needed?

Cooling from 60 to 55º

## results

The heat loss of a thermo mug without a cover is 9 W at those 60 º. Probably, the heat loss of the above-mentioned “smart cup” is the same (since the absence of a lid makes the main contribution to losses). And if the battery in the mug is less than 3 Wh • h (and even when discharged to zero), the smart mug will not last more than 20 minutes. That is no longer a closed thermomug.

## findings

1. In a typical ceramic coffee mug, it cools down from 60º to 55º in more than 6 and a half minutes, in a thermocup - almost 17 minutes.
2. A thermomug without a lid has almost no advantage over a conventional one.
3. As measurements have shown, the lid makes the greatest contribution, and not the walls of the circle.
4. As already mentioned in the comments to the main article, the best way is a massive thermocup that cools the drink from 90-95 ° C to a comfortable temperature. However, for the available materials (metal or ceramics) the mass will be too large to cool the drink to exactly 60. In this case, an interesting option would be a liquid filled mug. The drink would give the right amount of heat to the water in the walls, and then this increased mass of liquid kept the desired temperature longer. And if you make it possible to top up the coolant, you can set the desired temperature.

And if you drink tea or coffee with milk, the problem of the initial cooling is already solved.

So, if in addition to the smartphone, smart watches, headphones and so on, you do not want to charge the cup (!), Then a massive cup with a lid is your option.

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