This connects with essay 243, which is about smart meters for gas and electricity. If you don’t have one of these where you live, the meters output information to a hub, probably on the top of the new electricity meter, which then sends information off to the billing supplier at appropriate intervals. Included in each installation is an in-home device (IHD) which stores and outputs data to the user. Typical such devices give historic data by the day and by energy meter (gas, electricity, combined) both in money and in kWh.

My questions frequently ask you to make a conclusion about your answer. This is what arithmetic should do, inform an opinion. So I am asking you to express opinions once you find an answer. It is difficult for someone to say you are wrong in your opinion unless you misunderstand the number you produced; this should provide interesting class discussion of the sort that makes the subject feel worthwhile. I have also left room for different interpretations of what you could do with the numbers; do what you think is appropriate at the time.

1. On arrival downstairs in the winter, sufficiently early to beat the clock on the gas heating system, I see that the IHD records we have already spent 60p on energy today. What do you think this money represents? The 60p is made up of 34p electricity and 26p gas.

The IHD includes what is called the standing charge, which is £84 for electricity and £73 for gas. If the gas has not yet been used, how much used electricity is included above? In your house/room, what would that refer to?

2. I intend to boil the kettle. How much energy do I expect to use in boiling a half litre? Assume tap water temperature is 10º and that water requires 4184J per kg per degree C. If my kettle is rated at 2000W, how long do I expect this to take? Do you see anything wrong with this?

3. On another occasion I boil water in 70 seconds using a 3kW kettle. How much has this cost at 18.2p per kWh?

How much water do you think was in the kettle?

I looked up the average unit charges for gas and electricity. According to the EST, the Energy Savings Trust, Gas is 3.80 p/kWh and a standing charge of £87.23, while electricity at standard rate is 14.37p/kWh and with an annuual standing charge of £73.06. Using these averaged figures rather than the ones that apply in your house, look at these problems:

4. How much cheaper is gas than electricity? [Subtraction? Division? Decide!]

5. Figures from OfGem suggest that typical annual consumption is 16500kWh of gas and 3300kWh of electricity. Using these figures, find the typical annual total for these fuels.

Using the figures you generated, compare the annual cost per unit of gas as a percentage of that for electricity. How does this compare with your answer to Q4?

6. Gas consumption figures as measured by Ofgem dropped by 500 units per year every year in the period 2003 to 2011. If this continues, what sort of figure would you say this represents as an annual change per household? Please comment.

7. Between 2003 and 2011 OfGem says gas consumption went from 20,500 units to 16,500 units, while electricity stayed at 3300 units. What £ change would you expect them to report?

The report I found shows figures for gas of £608 in 2003 and £729 in 2011. What do you conclude?

8. The reduction in gas consumption between 2003 and 2011 produced little change at the domestic level, but when multiplied across the nation what does that represent? Gas prices rose by 15% in the five years 2012 to 2017, quite a bit faster than inflation. I found a prediction that prices will jump in 2018 and then rise more slowly. My interpretation suggests that the unit price 2018 will be 4.8p/unit and by 2023 5.2p/unit. If consumption continues at 16500, what do think the additional cost will be? You will probably need a table of results.

DJS 20180120

1. Mostly standing charge, which is similar for both fuels, £84 per year for E and £73 for gas. The extra 4 or 4.1p of electricity. 26x84/73=> 29.9p E standing charge.

2. Energy (J) = mass x 4184 J/º/kg x T change. A litre of water masses 1kg. So 0.5 x 4184 x 90º => 188280J = 188kJ. 188280/2000 = 94 secs. Did I need half a litre in the kettle and if I did, was that how much I put in? If it takes more than two minutes, something needs to change. Most of us put far too much water in the kettle.

3. 3 kW x 70/3600 = 0.0583kWh => 0.0583 x 18.2 = 1,06 p. 1sf okay

3kW x 70secs=210kJ = 4184 x 90 x M => 0.558kg = 0.558 litres, 98% of a pint. 1sf preferred, Answer ought to be "a pint". The timing may well go to the point at which the kettle switches off, which may be ( I tested this) 5 secs longer than with you listening to the kettle and switching it off yourself, so 10% error is quite likely. I did this for real using a pint, 67 secs to the point where the 3kW kettle swiched itself off.

4. 14.37/3.8 = 3.78 so nearly four times. Gas is 26% of the electricity price. If you want to include the standing charge, then you need to make some assumptions about annual total consumption, Q5.

5. (£87.23 + 16500 x 0.038) + (£73.06 + 3300 x 0.1437) = 714.23 + 547.27 = £1261.50

Gas 714.23/16500 = 0.0433, electricity 547.27/3300 = 0.1658, gas/elec => 26.10% 4sf, 2sf correct is good. The standing charge has no noticeable effect.

6. 500 kWh x £0.038 = £1.9 per year. Would people notice? As a money difference it probably disappears when compared with price changes. if people look at the kWh for their house, then you would notice that steady drop; in 2011 it was around 3% a year every year. 3% of the typical total energy cost is about £40; would many people notice? I doubt it, but what do you think?

7. 4000 x 0.038 = £152. I conclude that the price of gas changed too by about 20%. The published figures were (2003) £608/16500 => 3.68p/kWh and (2011) £729/20500=.3.56p/unit. If we assume a standing charge that did not change of £73 (it would have to change a lot to make a difference to the result), the money numbers change to £535 and £656, so that the unit rate numbers become 3.24p and 3.2p. Does that mean that gas went up in price after 2011, or perhaps that the EST 2017 number doesn’t agree with the OfGem 2011 number? Ofgem show a 15% rise in average standard price in the period 2012 to 2017, which would be equivalent to 3.3 to 3.8 pence per unit. The figures are pretty consistent.

8. 3% a year every year, as shown in Q6 answer.

Year Demand Rate Extra Cost

2017 16500 3.8 0

2018 16500 4.8 £165

2019 16500 4.9 + £16.5

2020 16500 5.0 + 2x£16.5

2021 16500 5.1 + 3x£16.5

2022 16500 5.2 + 4x £16.5

Total additional cost £165 + 10x£16.50 = £330. Similar answers all acceptable, but see how I made it look easy - that’s maths not arithmetic. The rise is about 2% a year once we get past the jump in 2018 (expected to be announced at the time of writing this!).

Those campaigning against the exploitation of shale for gas supply have not seen the predicted jump in gas price. Perhaps these are people for whom £200 extra a year is no big deal?