Exercises: Production and responsible use of energy

The Spanish electricity mix for one year can be approximated as follows: wind power $25\ \%$, nuclear power $20\ \%$, solar power $17\ \%$, combined cycle gas $15\ \%$, hydro power $12\ \%$ and other sources $11\ \%$, as shown in the graph.

1. a) Considering wind, solar and hydro power as renewables, what percentage of Spanish electricity was renewable?
2. b) Check that all the percentages in the mix add up to $100\ \%$.

Classify these energy sources as renewable or non-renewable, and justify your choice in each case: wind, coal, uranium, Sun, natural gas and biomass.

Producing $1\ \text{kWh}$ of electricity in Spain emits an average of about $0,15\ \text{kg}$ of $\text{CO}_2$ into the atmosphere. If a household consumes $300\ \text{kWh}$ in a month, how many kilograms of $\text{CO}_2$ correspond to that consumption?

A $10\ \text{W}$ LED light bulb gives the same light as a $60\ \text{W}$ incandescent bulb, as shown in the figure.

1. a) Calculate the energy each consumes if they are switched on for $5\ \text{h}$, in $\text{kWh}$.
2. b) Which of the two is more efficient? Explain using your results.

Household appliances carry an energy rating label with classes from A to G, as shown in the figure.

1. a) What does it mean if one refrigerator is class A and another is class G?
2. b) Explain why it is worth looking at this label before buying, even if the class A one is more expensive.

Burning one litre of petrol emits about $2,3\ \text{kg}$ of $\text{CO}_2$. If a car uses up a tank of $40\ \text{L}$, how many kilograms of $\text{CO}_2$ has it emitted?

Name two advantages and two disadvantages of solar photovoltaic energy as a way of producing electricity, and briefly explain each one.

A solar panel installation costs $4000\ \text{€}$ and saves $500\ \text{€}$ per year on the electricity bill. The graph shows the investment and cumulative savings:

How many years does it take to pay for itself, that is, to recover the money invested through the savings?

Spain's annual electricity demand is about $250\ \text{TWh}$. With last year's approximate mix (wind power $25\ \%$, solar power $17\ \%$):

1. a) How many $\text{TWh}$ were produced by wind power?
2. b) How many $\text{TWh}$ were produced by solar power?
3. c) How many $\text{TWh}$ did both add up to together?

A household consumes $3200\ \text{kWh}$ of electricity per year and the emission factor of the Spanish mix is $0,15\ \text{kg}$ of $\text{CO}_2$ per $\text{kWh}$.

1. a) Calculate the kilograms of $\text{CO}_2$ corresponding to that annual consumption.
2. b) Express it in tonnes.

A petrol car consumes $6\ \text{L}$ per $100\ \text{km}$ and travels $12000\ \text{km}$ per year. Burning one litre of petrol emits $2,3\ \text{kg}$ of $\text{CO}_2$.

1. a) How many litres does it consume in a year?
2. b) How many kilograms of $\text{CO}_2$ does it emit in a year? Express the result in tonnes as well, rounding to one decimal place.

In an entrance hall, $10$ incandescent $60\ \text{W}$ light bulbs are replaced with $9\ \text{W}$ LEDs. They are switched on for $4\ \text{h}$ a day for $365$ days a year.

1. a) How many $\text{kWh}$ are saved in a year? Round to one decimal place.
2. b) If the price is $0,16\ \text{€/kWh}$, how many euros are saved per year?

For a journey of $400\ \text{km}$, two options are compared per person:

• Petrol car consuming $6\ \text{L}$ per $100\ \text{km}$ with a single occupant ($2,3\ \text{kg}$ of $\text{CO}_2$ per litre).

• Electric train consuming $12\ \text{kWh}$ per passenger on that journey ($0,15\ \text{kg}$ of $\text{CO}_2$ per $\text{kWh}$).

1. a) Calculate the $\text{CO}_2$ emissions for the journey in each option.
2. b) How many times more does the car emit than the train in this case? Round to one decimal place.

A wind farm has a maximum capacity of $100\ \text{MW}$, but the wind does not always blow at the same speed, so its capacity factor (average percentage of maximum capacity) is $30\ \%$, as shown in the graph.

1. a) What is its average power output?
2. b) How much energy does it produce in a day, in $\text{MWh}$?

A detached house consumes $8000\ \text{kWh}$ of natural gas per year for heating. The emission factor of natural gas is $0,20\ \text{kg}$ of $\text{CO}_2$ per $\text{kWh}$.

1. a) How many kilograms of $\text{CO}_2$ does that heating emit per year?
2. b) If good insulation reduces consumption by $25\ \%$, how many kilograms of $\text{CO}_2$ are prevented from being emitted per year?

$6$ solar panels rated at $450\ \text{W}$ each are installed on the roof of a house. In that area, each installed kilowatt produces about $1500\ \text{kWh}$ per year.

1. a) How many kilowatts of power capacity do the panels add up to?
2. b) How many $\text{kWh}$ do they produce per year?
3. c) The household consumes $3600\ \text{kWh}$ per year: do the panels cover that consumption? How much energy is left over or short?

A solar panel installation costs $5000\ \text{€}$ and produces $4000\ \text{kWh}$ per year that the family no longer buys at $0,16\ \text{€/kWh}$.

1. a) How many euros does it save per year?
2. b) How many years does it take to pay for itself? Round to one decimal place.
3. c) If a grant covers $30\ \%$ of the installation, what is the new payback period?
4. d) The panels last about $25\ \text{years}$. How much money will have been saved in total over that time (without a grant)? Comment on whether the investment is worthwhile.

A nuclear power plant with a capacity of $1000\ \text{MW}$ operates for $8000\ \text{h}$ per year.

1. a) How much electrical energy does it produce in a year, in $\text{MWh}$? Express it in $\text{TWh}$ as well.
2. b) If that same energy were produced by burning gas, which emits $0,45\ \text{kg}$ of $\text{CO}_2$ per $\text{kWh}$, how many tonnes of $\text{CO}_2$ would be emitted? Nuclear power emits virtually no $\text{CO}_2$ when operating: how many tonnes does it avoid per year compared to gas?
3. c) State two advantages and two drawbacks of nuclear energy, and finish by giving your reasoned opinion on whether it should be part of the electricity mix.

A petrol car ($6\ \text{L}$ per $100\ \text{km}$; $2,3\ \text{kg}$ of $\text{CO}_2$ per litre) is compared with an electric car ($16\ \text{kWh}$ per $100\ \text{km}$; $0,15\ \text{kg}$ of $\text{CO}_2$ per $\text{kWh}$ with the current Spanish mix).

The graph shows the cumulative $\text{CO}_2$ for each car depending on the distance driven:

1. a) Calculate the kilograms of $\text{CO}_2$ per $100\ \text{km}$ for each car.
2. b) How many kilograms does each one emit per year if they cover $15000\ \text{km}$?
3. c) Manufacturing the electric car's battery emits about $6000\ \text{kg}$ of $\text{CO}_2$ more than manufacturing the petrol car. Using the emissions savings per $100\ \text{km}$, calculate after how many kilometres the electric car offsets the manufacturing of its battery. Round to the nearest thousand.
4. d) Using these results, write a short paragraph arguing when an electric car is worthwhile from an emissions point of view.

In the approximate Spanish electricity mix, combined cycle gas power plants produce $15\ \%$ of an annual demand of $250\ \text{TWh}$ and emit $0,45\ \text{kg}$ of $\text{CO}_2$ per $\text{kWh}$. The chart summarizes the mix data, present and future:

1. a) How many $\text{TWh}$ does gas produce today?
2. b) In a future scenario, wind power rises from $25\ \%$ to $35\ \%$ and gas falls from $15\ \%$ to $5\ \%$, with demand remaining constant. How many $\text{TWh}$ of gas are no longer produced?
3. c) How many tonnes of $\text{CO}_2$ would be avoided per year with this change? Express the answer in standard form.
4. d) Gas is usually used as backup when there is no wind or sun. Explain what technical problem would need to be solved to reduce it to a minimum and name a possible solution.

A home consumes $9000\ \text{kWh}$ of gas per year for heating, at $0,07\ \text{€/kWh}$. Insulating the façade costs $3000\ \text{€}$ and reduces consumption by $30\ \%$.

1. a) How much does heating cost per year before insulating?
2. b) How many euros does the insulation save each year?
3. c) What is the payback period for the investment? Round to one decimal place.
4. d) If a government grant covers $40\ \%$ of the insulation cost, what would be the new payback period? Comment on how grants influence energy savings decisions.

A family wants to reduce their carbon footprint. Their current situation:

• Electricity: $3800\ \text{kWh}$ per year ($0,15\ \text{kg}$ of $\text{CO}_2$ per $\text{kWh}$).

• Petrol car: $12000\ \text{km}$ per year with a consumption of $6,5\ \text{L}$ per $100\ \text{km}$ ($2,3\ \text{kg}$ of $\text{CO}_2$ per litre).

1. a) Calculate their current annual footprint by adding both items, in kilograms of $\text{CO}_2$.
2. b) They implement two measures: habit changes and LED lighting that save $700\ \text{kWh}$ per year, and car sharing, which halves the annual kilometres. Calculate the new annual footprint.
3. c) By what percentage have they reduced their footprint? Round to one decimal place and comment on which item contributed most to the reduction.

A village of $5000$ households wants to power itself using solar energy alone. Each household consumes on average $10\ \text{kWh}$ per day, and the panels in that area produce about $0,25\ \text{kWh}$ per day for every $\text{m}^2$ installed. The diagram shows the flow of energy between the panels, the households and the batteries:

1. a) How much energy does the village consume per day, in $\text{MWh}$?
2. b) How many $\text{m}^2$ of panels would be needed? Express the answer in hectares ($1\ \text{ha} = 10000\ \text{m}^2$) as well.
3. c) If $40\ \%$ of the consumption occurs at night, how much energy, in $\text{MWh}$, should the village's batteries store each day?
4. d) Outline two technical or land-use challenges of supplying a village using only solar power, and a possible solution for each.

An electric car consumes $16\ \text{kWh}$ per $100\ \text{km}$. Its footprint depends on how the electricity was generated (emission factors: current Spanish mix $0,15\ \text{kg}$ of $\text{CO}_2$ per $\text{kWh}$; coal-fired electricity $0,9\ \text{kg}$ of $\text{CO}_2$ per $\text{kWh}$). A comparable petrol car emits $13,8\ \text{kg}$ of $\text{CO}_2$ per $100\ \text{km}$.

1. a) Calculate the kilograms of $\text{CO}_2$ per $100\ \text{km}$ for the electric car using the current mix and using coal-fired electricity.
2. b) Compare the three cases: with which electricity source does the electric car emit even more than the petrol car?
3. c) Using these data, write a short argument in favour of the electric car and another one that qualifies this conclusion, mentioning the role of the electricity mix.

Unit challenge. How much energy does it take to heat water, and what environmental impact does it have depending on the time of day you do it?

1. Experimental measurement: Heat $m = (0,50 \pm 0,01)\text{ kg}$ of water in a microwave or electric kettle. Measure its temperature at regular intervals of $30\text{ s}$ for $2\text{ min}$ (with uncertainties of $\pm 1\text{ s}$ and $\pm 0,5\text{ }^\circ\text{C}$). Prepare a table with the data and plot $T$ versus $t$ to calculate the useful thermal energy transferred: $E = m \cdot c \cdot \Delta T$, with $c = 4180\text{ J/(kg}\cdot^\circ\text{C)}$.

2. Energy efficiency: Check the rated power ($P_{\text{nom}}$) on your appliance's label. Determine the electrical energy consumed ($E_{\text{cons}} = P_{\text{nom}} \cdot t$) and calculate the energy efficiency of the process: $\eta = (E / E_{\text{cons}}) \cdot 100\,\%$.

3. Electricity mix and proposal: Go to the Red Eléctrica de España (REE) website and record the renewable generation share and associated $\text{CO}_2$ emissions at that moment. Prepare a brief report with a reasoned proposal justifying the best consumption habits and schedules to minimize the environmental impact in your home.

Evaluation criteria:

• Rigor in taking home measurements, correct expression of uncertainties, and quality of the graph.

• Accuracy in calculating the useful energy transferred and the appliance's efficiency.

• Critical analysis of real REE data integrated into a responsible consumption proposal.