## Introduction: Energy Efficiency of Bringing Water to the Boil

When boiling water on a gas-fired stove three heat transfer mechanisms are in place: radiation, convection and conduction. Radiation and convection mainly occur between the flame and the bottom of the kettle or pan. Also, convection occurs when the flue gases escape and travel along the sides of the kettle. Conduction takes place where the bottom of the kettle touches its support.

When the gas is at minimum power (small flame) the combustion gases have more time to transfer their heat (through convection) to the pan compared to a situation where the gas is at maximum power (large flame). Moreover, the conduction losses through the kettle support may be less. This Instructable addresses the question whether the efficiency of a small flame is higher than the efficiency of a large flame.

The hypothesis tested in this Instructable is: with a small flame it will take less energy (i.e. less gas) to bring water to boiling temperature than it takes with a large flame. (The answer to this hypothesis can be found in Step 2)

The bonus question is: what is the average energy efficiency of boiling water on a gas stove? (The answer to this bonus question can be found in Step 3)

Not part of the initial research question is whether the amount of water in the kettle influences the efficiency of the process. But this was one of the unexpected outcomes of the experiments. (The answer to this second bonus question can be found in Step 4, which also features a discussion on the test setup)

To test the above hypothesis ten experiments were performed, five at minimum power and five at maximum power. In both series amounts of 200 g, 400 g, 600 g, 800 g and 1000 g (7.1 oz, 14.1 oz, 21.2 oz, 28.2 oz and 35.3 oz) were brought to boiling temperature. The mass is accurate to +/- 1 g (+/- 0.035 oz). The five water batches together each add to 3000 g (+/- 5 g) or 105.8 oz (+/- 0.2 oz).

The average starting temperature of the water was 13°C (55.4°F) and the average ambient temperature was 19°C (66.2°F). The time needed until reaching the boiling temperature (100°C or 212°F) was determined acoustically from the singing teakettle in which the experiments were performed. Time was measured in seconds using a stopwatch.

Step 5 in this Instructable does a suggestion for future work: the design of a condensing kettle to capture the latent heat in the flue gases.

In Step 6 some experiences from creating the graphs for this Instructable using Plotly (a collaborative data analysis and graphing tool) have been documented.The graphs are all available at www.plot.ly/~openproducts.

Step 7 finally spends some words on the CC BY license of this Instructable.

Take-home message
When bringing water to boiling temperature it is important to heat exactly the amount that is needed: boiling twice the volume of water needed means that half of the energy is going down the drain right away. Moreover, the boiling takes more time. The boiling process seems to become more efficient with a higher water level: using a smaller kettle or pan and filling it up completely is more efficient (and thus quicker) than a larger one that is mostly empty. Finally, it is of key importance to close the lid of the pan during the process to avoid convective and evaporative energy losses. The graphs in this Instructable have been generated using Plotly, which is a professional and convenient browser-based graphing environment, ideal for sharing data.

Previously openproducts released other Instructables in which energy efficiency and reduction of natural gas consumption was addressed: One-Armed Bandit - Mixer Tap Redesign (CC BY, 14 June 2013) and Energy Saving by Omitting Stand-by Energy Use in Combi Boiler through Remote Switches (CC BY, 30 July 2012).

The release of this Instructable (and all others) has been announced on Twitter.

## Step 1: Data: Measured Time

The times recorded for bringing the various amounts of water to boiling temperature have been presented below.

`Experiment ; Power ; Mass ; Time ;    #      ; stove ;  [g] ;  [s] ;    1      ;  Max  ;  200 ;  140 ;    2      ;  Max  ;  400 ;  246 ;    3      ;  Max  ;  600 ;  362 ;    4      ;  Max  ;  800 ;  460 ;    5      ;  Max  ; 1000 ;  563 ;    6      ;  Min  ;  200 ;  620 ;    7      ;  Min  ;  400 ; 1050 ;    8      ;  Min  ;  600 ; 1530 ;    9      ;  Min  ;  800 ; 1920 ;   10      ;  Min  ; 1000 ; 2280 ;`

In the case with the minimum power the point in time at which the water is boiling (i.e. when the kettle is singing) was difficult to determine: the flute started too gently to be attributed to a specific end time. It would have been more accurate to measure the temperature of the water.

The next step presents the measured gas consumption.

## Step 2: Data: Gas Consumption and Interpretation of the Experiments

In addition to the above time data, the gas consumption is an important parameter. This was measured using a standard gas volume meter.

At minimal flame it cost 69.5 liter (4241 cu in) of natural gas to bring the 3000 g water in five separate experiments to boiling temperature. In the five experiments at maximum flame it cost 69.0 liter (4210 cu in) to boil exactly the same amount (in considerably less time).

Thus, it can be concluded that the smaller flame is not more efficient than the large flame.

Knowing the total gas consumption for each of the series of five experiments it is possible to attribute a gas consumption to each of the experiments (because the gas flow has been constant during the experiments). In the data overview below '~M~' indicates ‘Measured Value’ and '~C~' means ‘Calculated Value’.

`Experiment ; Power ; Mass ;   Time   ;    Gas     ;    #      ; stove ;  [g] ;    [s]   ;  [liter]   ;    1      ;  Max  ;  200 ;  140 ~M~ ;   5.45 ~C~ ;    2      ;  Max  ;  400 ;  246 ~M~ ;   9.58 ~C~ ;    3      ;  Max  ;  600 ;  362 ~M~ ;  14.10 ~C~ ;    4      ;  Max  ;  800 ;  460 ~M~ ;  17.92 ~C~ ;    5      ;  Max  ; 1000 ;  563 ~M~ ;  21.94 ~C~ ;Total Max  ;  Max  ; 3000 ; 1771 ~C~ ;  69.0  ~M~ ;    6      ;  Min  ;  200 ;  620 ~M~ ;   5.82 ~C~ ;    7      ;  Min  ;  400 ; 1050 ~M~ ;   9.86 ~C~ ;    8      ;  Min  ;  600 ; 1530 ~M~ ;  14.37 ~C~ ;    9      ;  Min  ;  800 ; 1920 ~M~ ;  18.03 ~C~ ;   10      ;  Min  ; 1000 ; 2280 ~M~ ;  21.41 ~C~ ;Total Min  ;  Min  ; 3000 ; 7400 ~C~ ;  69.5  ~M~ ;`

The calculated values for gas consumption in each experiment will be used in the further analysis in the next steps.

## Step 3: Determining the Efficiency of a Gas Stove

On average over the ten experiments, an amount of (69.0 + 69.5 =) 138.5 liter natural gas has been used to bring (3000 + 3000 =) 6000 g (211.6 oz) of water to boiling temperature.

The energy input Qgas [J] from gas volume v equaling 138.5 liter (0.1385 m3) of natural gas (assuming an energy content e of 31.65 MJ/m3, lower heating value) amounts to:

Qgas = 4.38 MJ

The energy Qwater [J] used for heating the water can be determined using an expression

Qwater = m c delta T

With m = 6000 g, c = 4.186 J/gK and delta T = 87 K this boils down to:

Qwater = 2.19 MJ

Consequently, the average efficiency can be put at eta = Qwater/Qgas = 2.19 / 4.38 = 50%.

Taking into account uncertainties in the measurements (m: +/- 10 g, delta T: +/- 1 K, e: +/- 5%, v = +/- 10%) the efficiency eta may range from 43% to 59%.

The calculation takes the total water volume as an input and the total gas volume consumed.

The calculation can be repeated for each of the experiments, resulting in the table below, also presented graphically in above figure. The interpretation of the figure will be done in the next step.

`Mass                    ; 200;  400;  600;  800; 1000; g   ;Theoretical             ; 364;  364;  364;  364;  364; J/g ;Measured, minimum power ; 921;  780;  758;  713;  678; J/g ;Measured, maximum power ; 863;  758;  744;  709;  694; J/g ;`

The next step elaborates on the test setup and brings up new insights.

## Step 4: Discussion

The efficiency calculated in step 3 (50%) is not very high.

Factors that are uncertain are the energy content of the natural gas, which varies during the year and across regions. Also, it might be that the volume v of the natural gas has not been determined accurately due to the relatively low ambient temperature of the measuring device (approximately 10 °C ( 50 °F) at the time of the experiment. This would have affected the energy content upward, resulting in an even lower efficiency. Or perhaps the flow has not been sufficient for accurate measuring (see picture: the meter plate reads ‘Qmin=0.04 m3/h’, i.e. 40 liter per hour).

Another factor that can have determined the experiment is the way in which the timing has taken place: reaching boiling temperature has been determined acoustically, based on the flute of the singing kettle. As this flute requires quite some flux of steam it might take considerable additional energy to generate this. As a matter of fact, energy is used to vaporize part of the water. This means that the experiment setting is less suited for determining the stove efficiency (the bonus question), but still appropriate for answering the hypothesis in this Instructable on the difference between minimum and maximum power.

The experiment in this Instructable has been performed under indoor conditions. Outside, for example on a camping, wind can seriously influence the efficiency of a gas pit. This could be an indication that the convective heat transfer still has an important function.

From the graphs the effect of the water volume has been introduced in the previous step. The underlying mechanism could be that when the water level is too low it is more difficult for a mixing flow to start. Higher water levels might ease the mixing process, possibly assisted by the hot side of the kettle, caused by convection heat transfer.

Finally, for energy efficiency reasons it is of key importance to close the lid of the pan during the process to avoid convective and evaporative energy losses. And yes, this also holds when cooking pasta.

Data According to the Stove’s Manual
Comparing the measured data to the specifications in the stove manual some differences can be observed. For example, the maximum gas consumption is 0.221 m3/h (0.06 liter/s), whereas the experiment shows 0.04 liter/s in the maximum case. This may be an indication that the nozzle is filthy. The manual indicates that the stove power ranges from 0.40 kW to 2 kW (factor 5) but the measurements indicate a factor 4 difference (approximately 0.3 kW at minimum flame and 1.2 kW at maximum flame, calculated by dividing the estimated gas consumption (kJ) by the duration (s) of the experiments).

For the take-home message at the beginning of this Instructable it is also important to heat exactly the amount of water that is needed for your purpose: all energy invested without being used in the end is thus useless. This is also a quick win for reducing energy efficiency of water heaters. Also it is of key importance to close the lid of the pan during the process to avoid convective and evaporative energy losses.

If you are interested in energy efficiency and reducing natural gas consumption perhaps two other openproducts Instructables are relevant: One-Armed Bandit - Mixer Tap Redesign (CC BY, 14 June 2013) and Energy Saving by Omitting Stand-by Energy Use in Combi Boiler through Remote Switches (CC BY, 30 July 2012).

The next step addresses further work.

## Step 5: Future Work

All in all, it would be interesting to try to increase the efficiency of the stove by trying to exploit the higher heating value of the gas instead of the lower heating value by an innovative kettle design, capturing and condensing the energy from the vapor (see picture: in the beginning of the boiling process the cold side of the kettle causes condensing of the vapor in the flue gas). Exploiting the higher heating value of natural gas might yield some percentages of efficiency gain. However, when only focusing on the lower heating value there is a lot to be gained already.

The next step addresses the experiences of making the graphs for this Instructable using plotly.

## Step 6: Experiences Using Plotly

Plotly is a collaborative data analysis and graphing tool, accessible through a web browser. Expectedly it is very powerful in data processing, data analysis and data visualization. This Instructable only makes use of the graphing facility but it should be very well possible to perform all calculations within the tool. (Interested readers may want to reproduce all graphs using scripting: the starting point is the very few measured data introduced in Step 1 and 2 of this Instructable.) Only very few introduction is needed to get started with #plotly, and the control works quite intuitively. Features that were found particularly interesting and differ from spreadsheet tools:

• Easy filling area below lines;
• Easy stacking multiple figures (see figure above);
• Easy export of graphs to scalable vector graphics (SVG);
• Consequently, easy post-processing of the image, for example using Inkscape;
• Easy sharing of data.

As mentioned before, the data and graphs from this Instructable are all available at www.plot.ly/~openproducts.