A lesson in practical thermodynamics.
Maarten Ambaum (email@example.com)
Mark Prosser (firstname.lastname@example.org)
Everybody knows that the key boundary condition for a successful PhD is the provision of plenty of coffee during the day (tea, for some). Our Department has a hot water boiler with a 10 litre water tank capacity to provide an unlimited supply of hot water (it is connected to the tap to keep it topped up automatically). For historical reasons we actually call it the “urn” – I like that word so we stick to it here.
When we got a new urn recently (a “Marco Ecoboiler T10”) we were intrigued to see it had an ECO mode button, presumably promising a lower energy consumption. Indeed, when anyone in the morning saw that the urn was not in “ECO mode”, it was swiftly switched on; green credentials and all that.
One of our postdocs dug up the specs from the internet, where we learned that “ECO mode” actually makes the urn operate with 5 litres of water, which is half full. The specs suggest that when switching the urn on you then only need to heat half the amount of water. But is there more to it? Would the urn working with a half-full tank actually use less energy?
I teach atmospheric physics to our Masters and PhD students and this is precisely the kind of question I would ask them to think about. In fact I sent out an email to all members of the Department, and it turned out that there were different opinions, even amongst those who should know better, although in my view obviously only one physically correct outcome.
So, let us find out. First some theory (some basic thermodynamics), then experiment, and conclusions at the end.
One of the first things we learn in thermodynamics is conservation of energy: energy in equals energy out. The energy in is the electrical power that the urn uses, the energy out is the hot water we consume, heated up from around 15C to around 95C, as well as thermal losses, and running the internal electronics of the urn. The last bit is very marginal, just a controller and a few LEDs. We are going to ignore that. The thermal loss may well be substantial, but the water tank of the urn is actually quite well insulated with Styrofoam, so who knows.
Given that we drink the same amount of coffee, whether the urn is in ECO mode or not, the energy cost for producing the hot water does not depend on whether we run at half tank capacity or full tank capacity. We still need to heat up the same amount of water for our coffee consumption.
What is left is the energy loss. But the energy loss is proportional to the temperature difference between the inside of the tank and the outside. The inside of the tank remains close to 95C all the time, so it looks like the energy loss also cannot depend on whether we are in ECO mode or not.
Energy in equals energy out, energy out remains the same, so energy in should remain the same, ECO mode or not.
Did we miss something? Surely, a feature that is advertised as ECO mode should consume less energy?
We should give the manufacturer some credit. They claim: “This mode saves energy by minimising the energy wasted during machine down-time. The ECO mode is most effective in installations where the machine has a regular ‘off’ period.” Perhaps; perhaps not.
Unfortunately they also claim: “During the ‘off’ period as there is less water in the tank there will be less energy lost to the surrounding environment resulting in an energy saving.” This latter claim is a tricky one: Energy loss is proportional to the temperature difference between the tank and the exterior irrespective of how much water is in the tank. As the heat capacity of the full tank is higher, it will reduce its temperature more slowly, possibly leading to a higher total energy loss, as the temperature differential is kept higher on average for a full tank. So after switching on the urn again, this increased energy loss needs to be topped up. Is that then the way ECO mode helps us being green?
We did what any scientist would do, faced with such a question: do the experiment; this is where Mark comes in. Easy enough: these days you can buy power adaptors that plug in the wall socket and accumulate the total amount of electrical energy used over some period.
We did four experiments: two midweek ones running for three consecutive 24 hour periods from Tuesday to Thursday, two weekend ones running from 6pm on Friday to 9am on Monday. In half of the experiments we left the ECO mode button on, and in the other half, the ECO mode button was left switched off.
Straight to the results:
|ECO mode||Non-ECO mode|
|Midweek (3 days)||21.77 KWh||20.25 KWh|
|Weekends||4.2 KWh||4.05 KWh|
Lo and behold: it does not make much difference at all and, if anything, ECO mode uses more energy!
Of course the experiment is not carefully controlled: perhaps we drank more coffee during the ECO mode periods, but both weeks were pretty similar in coffee room usage, there were no big events, and the two weekends were pretty much completely quiet. In fact the weekend usage is probably dominated by the usage before 9am on a Monday. We have cleaners that come in very early, and there are quite a few members of staff that come in before nine in the morning, and perhaps even some PhD students!
Let’s do some more analysis of the data: daily normal usage is about 7KWh per day, as in the midweek data. That means that from the 4.1KWh weekend usage less than about 1KWh (about one seventh of a normal day’s usage to account for the Monday am usage – I know it is a rough estimate) corresponds to normal usage, and the rest is energy loss when the urn is switched on but not used. I estimate the loss to be 1.7KWh per day, so that a weekend, including the Monday early rush hour, corresponds to about 3.4KWh losses and about 0.7KWh normal usage.
So, from the 7KWh daily energy usage, about 1.7KWh is thermal energy loss (and other bits and bobs, such as the lovely LEDs at the front of the urn), with an error bar, I guess, of possibly 30%. Is this a lot of energy loss? 1.7KWh per day corresponds to 70W loss, about the same as the lighting of a single-person office. Not bad. The Marco Ecoboiler is probably pretty “eco”, but not because of its ECO mode.
We are then left with 5.3KWh each day to make coffee. A coffee cup is about 200ml, and assuming the water for the coffee needs heating from 15C to 95C, each cup of coffee requires 0.2kg x 80K x 4200 J/kg/K = 67KJ of energy, or 0.019KWh. That means that 5.3KWh corresponds to about 280 cups of coffee per day. Probably quite realistic, given the size of our Department.
Should we switch off the urn overnight? Well, an overnight period (all losses, as there is no usage of the urn, perhaps for about 11 hours) would use about 0.8KWh. But, of course, the tank will have cooled down, perhaps to 30C, and needs reheating to 95C. This costs for a 10 litre tank about 0.8KWh. Funny that is: probably better to just leave the tank on overnight to prevent people from using highly inefficient kitchen kettles, and prevent people from having to wait for the urn to heat up in the morning.
Actually, this is not as much coincidence as it may seem: the thermal loss during the night switch off period must of course equal the loss in thermal energy of the water, which then needs to be replenished when we reheat the water back to 95C.
As I said before, the full tank could well lose more energy as it keeps relatively warmer during the cooling off period compared to the half full tank of ECO mode. But a quick calculation, assuming a well-insulated tank, shows that the temperature reduction is proportional to (T0-Te) / k with T0 the initial tank temperature (95C), Te the external temperature, and k the heat capacity of the tank. So, indeed, a full tank, with larger k, has a smaller temperature reduction with time, and remains warmer on average. But the energy cost of this reduction of course equals the heat capacity k times the change in temperature: k x (T0-Te) / k = (T0-Te), so we get an energy loss proportional to (T0-Te), but independent of the heat capacity k of the tank. It looks like the engineers at the manufacturers overlooked some basic physics.
By the way: how long would it take to reheat the tank in the morning if it had cooled down to 30C overnight? Well, at full pelt the urn uses 2.8KW, so a required energy of 0.8KWh takes about 15 minutes to produce. Pretty long wait. Probably not worth the frustration.
So, to conclude: our Ecoboiler is quite “eco”: it wastes only about 70W in thermal losses, not so bad for a Department that uses big computing resources (not so “eco”).
The thermal energy losses from the urn are pretty modest in the grand scheme of things, and it turns out to be better to just leave the urn on overnight, as the cost of reheating the cold urn in the morning is nearly the same as the energy cost of leaving it on. Leaving the urn on over the weekend is probably also better than switching off, because the occasional weekend user will end up using a highly inefficient kitchen kettle.
The “ECO mode” button makes the urn operate at half tank capacity, but the thermodynamical arguments as well as the measurements show that it actually uses at least the same amount of energy in ECO mode. In fact, at half capacity the tank has more steam in it, and the steam is possibly slightly hotter, on average, than the liquid, and thus more energy may be lost through conduction. Just leave the ECO mode button switched off; it doesn’t do any good.