Estimating the energy used in everyday life

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 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.

On a monthly bill, the consumption is $240\ \text{kWh}$ and the price per kilowatt-hour is $0,17\ \text{€/kWh}$. How much does that energy cost?

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?

Each litre of petrol contains a chemical energy of about $9,5\ \text{kWh}$.

1. a) A car consumes $6\ \text{L}$ every $100\ \text{km}$: how much energy, in $\text{kWh}$, does it use on that journey?
2. b) Express the car's consumption in $\text{kWh/km}$.

A home consumes $4200\ \text{kWh}$ per year, while the average consumption of Spanish households is around $3500\ \text{kWh}$ per year, as shown in the graph.

1. a) By what percentage does that home exceed the average consumption?
2. b) If $30\ \%$ of that home's consumption corresponds to electric heating, how many $\text{kWh}$ is that?
3. c) Turning the thermostat down by one degree saves $10\ \%$ of heating energy. How many $\text{kWh}$ and how many euros (at $0,17\ \text{€/kWh}$) would be saved per year?

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 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.