Exercises: Energy and its consumption

Explain the difference between a renewable and a non-renewable energy source (whether or not it runs out on a human time scale) and write down three examples of each type, indicating where each one is obtained from.

The figure classifies some energy sources into two families, but one non-renewable source is missing.

The missing source burns nothing, but it uses uranium and produces very long-lasting radioactive waste. Name it and add it to the classification, explain the criterion that separates the two families, and classify these four sources: biomass, tidal energy, coal and the heat from the Earth's interior.

Explain what an energy transformation is using two examples from your life:

1. a) A lamp that is switched on.

1. b) Pedaling a bike.

In each case, state which energy goes in and which energy comes out.

The figure shows the chain of transformations of a hydroelectric dam, with one machine covered.

Between the turbine and the grid there is a machine that converts the rotation into electricity. Name it, explain what energy transformation occurs in each link of the chain, and reason why electricity is not an energy source, but a way of transporting energy.

Explain in your own words what the kilowatt-hour (kWh) measures and why it is the unit on the electricity bill: it combines how much power an appliance has with how long it is running. Give an example of an appliance of $1\ \text{kW}$ switched on for one hour.

Explain what information an appliance's energy label provides: the efficiency rating letter (from A to G) and the estimated annual consumption. Which letter would you choose between two similar models and why is it not enough to look at the price alone?

Explain what energy efficiency is using the example of LED light bulbs: they provide the same light while consuming much less electricity because they lose hardly any energy as heat. Where is energy "lost" in an old light bulb?

List three energy-saving measures at home (turning off lights and standby appliances, turning down the heating by one degree, using short programs on the washing machine) and explain what each one changes: less power, less operating time or fewer losses.

Describe the chain of transformations in a gas thermal power station: chemical energy of the fuel → thermal energy upon burning it → kinetic energy of the steam and turbine → electrical energy in the alternator. Explain what happens at each link and where most energy is lost as heat.

The Sun and wind are not always available. Explain what the intermittency of renewables is, what three solutions offset it (reservoirs storing water, batteries, combining several sources in the grid) and why we cannot rely on a single source.

The figure shows a simplified energy label and the details of a fridge with its annual consumption covered up.

The fridge consumes an average of $100\ \text{W}$ and is connected for $24$ hours. Calculate its consumption in one day and in one year in kWh, estimate the annual cost at $\$0.15$ per kWh and explain which two details on the label you would compare before buying a new one.

A ceramic cooktop of $1,200\ \text{W}$ is used for $1$ hour a day. Calculate its consumption in a $30$-day month in kWh and its cost at $\$3$ per kWh, showing the steps (power in kW, energy for the month, cost), and compare the result with what charging a cell phone consumes each day, knowing that each full charge uses about $12\ \text{Wh}$.

Two similar fridges: one with rating A that consumes $150\ \text{kWh}$ per year and costs $\$13\,000$, and another with rating D that consumes $350\ \text{kWh}$ per year and costs $\$10\,000$. Calculate the annual electricity expenditure for each at $\$3$ per kWh, the annual savings of model A, and in how many years the price difference is recovered. Which one would you buy?

A television on standby consumes $3\ \text{W}$ for $20$ hours a day. Calculate its annual consumption in kWh and its cost at $\$3$ per kWh, explain what "vampire draw" is and propose a simple solution for the whole house (a power strip with a switch).

A kWh does not always "pollute" the same: it depends on which sources were used to generate it at that moment (the energy mix). Explain why consuming electricity when the wind is blowing or the sun is shining results in lower emissions than during peak hours without renewables, and what habit you can change at home to take advantage of this.

Carry out a mini-audit of your school: identify four wastes of energy (lights turned on with nobody present, screens on standby, heating on with open windows, old equipment) and propose a measure for each one, ranking them by the impact you think they would have.

A coastal municipality near a mountain range consumes a constant base load of $8\ \text{MW}$, but records peaks of $18\ \text{MW}$ on winter nights (due to heating) and $22\ \text{MW}$ at midday in summer (due to tourism and air conditioning). It has a wind farm in the mountains, a solar photovoltaic plant, and a natural gas combined-cycle power plant. Design and justify the generation breakdown by assigning each technology a clear role (base load, peak following, or security reserve) to prevent blackouts with the lowest possible environmental impact. Explain in detail how the system should respond during three consecutive winter days covered by a windless storm.

A user posts on social media: "A gas thermal power plant that harnesses $38\ \%$ of the fuel's energy is an engineering bungle; at my house, an electric radiator has an efficiency of $100\ \%$ because it converts all electricity into heat."

1. a) Technically refute this statement: describe the chain of energy transformations in the thermal power plant and justify at which points inevitable thermal losses occur according to the laws of thermodynamics.
2. b) If we replace the gas plant with a wind farm that harnesses $40\ \%$ of the wind's energy, explain why that $40\ \%$ efficiency does not entail the same economic or environmental cost as the $38\ \%$ of the thermal plant.

A country with high renewable penetration must decide whether to extend the lifespan of its nuclear reactors by $10$ years or disconnect them immediately and use gas power plants as backup while installing more batteries and wind farms.

1. a) Analyse the technical and environmental dilemma by evaluating two opposing criteria: the immediate reduction of greenhouse gases versus the long-term problem of high-level radioactive waste.
2. b) From the standpoint of electrical grid stability, what operational drawback would relying exclusively on solar and wind present without the continuous support of a firm synchronous source such as nuclear or gas? Formulate and justify your technical recommendation.

A family spends $\$2,400$ per year on electricity in a poorly insulated home ($70\ \%$ on heating, $15\ \%$ on hot water, and $15\ \%$ on home appliances and lighting). They have a budget of $\$3,000$ to improve the home and are hesitating between two options:

• Option A: Replace old home appliances with Class A appliances and LED lighting (cost: $\$2,500$; estimated savings: $30\ \%$ of the consumption in home appliances and lighting).

• Option B: Install thermal insulation on ceilings and seal air leaks around windows (cost: $\$2,800$; estimated savings: $25\ \%$ of heating consumption).

1. a) Calculate the annual economic savings of each option and how many years it will take the family to pay off each investment.
2. b) Technically justify why improving the building envelope is usually a much higher priority than replacing consuming appliances.

A home consumes $3,500\ \text{kWh}$ per year. The family installs solar panels for $\$4,200$ that produce $3,000\ \text{kWh}$ annually. The electricity they buy from the grid costs $0.20\ \text{\$/kWh}$ and the utility company compensates surplus electricity fed into the grid at only $0.06\ \text{\$/kWh}$.

1. a) If the family is away during daylight hours and only directly self-consumes $30\ \%$ of the solar energy generated (feeding the remaining $70\ \%$ into the grid), calculate the annual savings achieved and the years needed to pay off the installation.
2. b) If they schedule the water heater, washing machine, and dishwasher to increase direct self-consumption to $70\ \%$ (feeding only $30\ \%$ into the grid), recalculate the savings and the new payback period. Explain the reason for the economic difference if the total solar production has been identical.

A city council can only fund one solar photovoltaic installation without batteries and must choose between the roof of a secondary school (operating hours from $8{:}00$ to $15{:}00$, Monday to Friday) or that of a municipal sports center (operating hours from $16{:}00$ to $23{:}00$ every day).

1. a) Roughly sketch or describe the overlap between the hourly solar production curve and the consumption curve of each building. Justify in which of the two buildings direct self-consumption will be much more profitable and efficient.
2. b) The school has a major drawback: it is not in operation on weekends or during July and August, when solar production is at its peak. Propose two technical or management solutions to harness those seasonal surpluses for the benefit of the community without installing expensive chemical batteries.

The following items appear on a household's monthly electricity bill before taxes:

• Power term: $5.75\ \text{kW}$ contracted at $0.11\ \text{\$/(kW}\times\text{day)}$ for $30$ days $\rightarrow \$18.98$.

• Energy term: $180\ \text{kWh}$ consumed at $0.18\ \text{\$/kWh} \rightarrow \$32.40$.

The power control switch (ICP) has never tripped, and the two highest-power appliances in the house are the oven ($2.0\ \text{kW}$) and the washing machine ($1.8\ \text{kW}$).

1. a) If they reduce the contracted power to $4.0\ \text{kW}$ and decrease their consumption by $30\ \text{kWh}$ per month by turning off devices on standby, calculate the monthly financial savings before taxes.
2. b) Explain the technical difference between the two billed concepts: why the power term is paid even if the house is empty for a month, and what habit they should adopt with their household appliances so as not to exceed $4.0\ \text{kW}$.

Comment on the statement "the cheapest and cleanest energy is the energy that is not consumed": compare two strategies of a municipality — installing more renewables or reducing consumption through efficiency (LED streetlights, insulating public buildings) — and defend with arguments which one you would implement first and why.