Estimating the energy used in everyday life

A microwave oven has a power rating of $0,8\ \text{kW}$ and operates for $0,5\ \text{h}$, as shown in the graph.

1. a) Calculate the energy it consumes, in $\text{kWh}$.
2. b) Is the kilowatt-hour a unit of power or energy? Justify your answer based on how it is calculated.

Knowing that $1\ \text{kWh} = 3,6\cdot10^{6}\ \text{J}$, express an energy of $4\ \text{kWh}$ in joules. Give the result in standard form.

A refrigerator has an average power rating of $150\ \text{W}$ and is plugged in $24\ \text{h}$ a day. How much energy does it consume in a day, in $\text{kWh}$?

On Irene's home electricity bill, the meter reading is shown: previous reading $14520\ \text{kWh}$, current reading $14835\ \text{kWh}$, as shown in the figure.

1. a) How many kilowatt-hours has the family consumed in that period?
2. b) Explain how this figure is obtained from the two readings.

A household consumes an average of $320\ \text{kWh}$ per month. What is its annual consumption, in $\text{kWh}$?

An electricity bill has two parts: a fixed standing charge for power of $24\ \text{€}$ per month and an energy charge of $0,16\ \text{€/kWh}$, as shown in the diagram.

1. a) If the consumption for the month was $300\ \text{kWh}$, what is the total amount of the bill, excluding taxes?
2. b) What percentage of the total corresponds to the standing charge? Round to one decimal place.

A family's bi-monthly electricity bill shows a consumption of $460\ \text{kWh}$.

1. a) Estimate the household's annual consumption, assuming all two-month periods are equal.
2. b) If the average price is $0,16\ \text{€/kWh}$, how much does the family spend on electricity per year?

An electric oven rated at $2,2\ \text{kW}$ is switched on for $45\ \text{min}$ to cook dinner.

1. a) Calculate the energy consumed, in $\text{kWh}$ (be careful with the units of time).
2. b) If the price is $0,20\ \text{€/kWh}$, how much does cooking that dinner cost?

Nerea's family carries out an energy audit of their home. Estimate the monthly consumption ($30$ days) of each appliance:

• Electric water heater: $1,5\ \text{kW}$ for $3\ \text{h}$ a day.

• Refrigerator: $100\ \text{W}$ for $24\ \text{h}$ a day.

• Washing machine: $1\ \text{kW}$ for $1\ \text{h}$ a day.

• Ceramic hob: $1,2\ \text{kW}$ for $1\ \text{h}$ a day.

• Lighting: $60\ \text{W}$ for $5\ \text{h}$ a day.

The graph compares the power rating of each appliance with its hours of use:

1. a) Calculate the monthly $\text{kWh}$ for each item.
2. b) Sum the estimated total consumption.
3. c) The actual bill is around $250\ \text{kWh}$ per month. If the estimate does not match the bill, explain what this could be due to.
4. d) Identify the two items that consume the most and propose a specific measure to reduce each one.

A shower uses $50\ \text{L}$ of water ($50\ \text{kg}$) that needs to be heated from $15\ ^\circ\text{C}$ to $35\ ^\circ\text{C}$. The specific heat capacity of water is $c_e = 4180\ \text{J/(kg}\cdot^\circ\text{C)}$.

The figure summarises the data for heating the water:

1. a) Calculate the required energy, in joules, using $Q = m\cdot c_e\cdot\Delta T$.
2. b) Convert it to $\text{kWh}$, knowing that $1\ \text{kWh} = 3,6\cdot10^{6}\ \text{J}$, and round the result to one decimal place.

Four people live in Ionut's house and each takes a daily shower using $60\ \text{L}$ of water ($60\ \text{kg}$) heated from $14\ ^\circ\text{C}$ to $34\ ^\circ\text{C}$. The specific heat capacity of water is $c_e = 4180\ \text{J/(kg}\cdot^\circ\text{C)}$.

1. a) Calculate the energy of one shower using $Q = m\cdot c_e\cdot\Delta T$ and express it in $\text{kWh}$, rounding to one decimal place (remember: $1\ \text{kWh} = 3,6\cdot10^{6}\ \text{J}$).
2. b) How many $\text{kWh}$ does the family consume in showers during a $30$-day month?
3. c) How much do these showers cost per year if the average price is $0,15\ \text{€/kWh}$?

A commuter train consumes $300\ \text{kWh}$ on a journey of $50\ \text{km}$ carrying $150$ people.

1. a) How much energy corresponds to each passenger on that journey?
2. b) Express the consumption in $\text{kWh}$ per $100\ \text{km}$ per passenger.

A group of friends wants to go on a trip of $300\ \text{km}$ and compares three options (each litre of fuel is equivalent to $9,5\ \text{kWh}$):

• Petrol car consuming $6\ \text{L}$ per $100\ \text{km}$, with $2$ occupants.

• Bus consuming $30\ \text{L}$ per $100\ \text{km}$, with $40$ passengers.

• Electric train consuming $3000\ \text{kWh}$ for the entire journey, with $200$ passengers.

The diagram summarises the data for the three options:

1. a) Calculate the total energy of the journey for each option, in $\text{kWh}$.
2. b) Calculate the energy per passenger for each option and order them from lowest to highest consumption.
3. c) The car is the worst option with $2$ occupants. How would the result change if $4$ people travelled in it? Justify your answer with the calculation.

A family has a time-of-use electricity tariff: energy during off-peak hours costs $0,10\ \text{€/kWh}$ and during peak hours $0,22\ \text{€/kWh}$. In one month, they consume $200\ \text{kWh}$ off-peak and $100\ \text{kWh}$ peak.

1. a) Calculate the cost of energy for that month.
2. b) If the family manages to shift $50\ \text{kWh}$ from peak to off-peak hours (for example, by running the washing machine at night), what would the new cost be?
3. c) What percentage saving does this change of habits represent? Round to one decimal place.