Exercises: Estimating energy consumed 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 $1\ \text{kWh} = 3.6\times10^{6}\ \text{J}$, 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 $3.40\ \text{\$/kWh}$. How much does that energy cost?

A car consumes $6\ \text{L}$ of gas every $100\ \text{km}$ and its tank holds $42\ \text{L}$. How many kilometers can it travel on a full tank?

A city bus consumes $35\ \text{L}$ of diesel every $100\ \text{km}$ and carries $50$ passengers.

1. a) How many liters per $100\ \text{km}$ correspond to each passenger?
2. b) Compare this value with $7\ \text{L}$ per $100\ \text{km}$ for a car with only the driver traveling, and comment on the result.

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 $\text{kWh}$?

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

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 $3.20\ \text{\$/kWh}$, 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 $4\ \text{\$/kWh}$, how much does cooking that dinner cost?

Each liter of gas 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 trip?
2. b) Express the car's consumption in $\text{kWh/km}$.

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 $c_e = 4180\ \text{J/(kg}\times^\circ\text{C)}$.

The figure summarises the data for heating the water:

1. a) Calculate the required energy, in joules, using $Q = m\times c_e\times\Delta T$.
2. b) Convert it to $\text{kWh}$, knowing that $1\ \text{kWh} = 3.6\times10^{6}\ \text{J}$, and round the result to one decimal place.

An electric heater rated at $1.5\ \text{kW}$ is turned on for $6\ \text{h}$ a day during a $30$-day month.

1. a) How many $\text{kWh}$ does it consume in a month?
2. b) How much does that heating cost per month if the price is $3\ \text{\$/kWh}$?

An airplane consumes $1600\ \text{L}$ of kerosene on a flight of $400\ \text{km}$ carrying $160$ passengers.

1. a) How many liters correspond to each passenger on that flight?
2. b) Express the consumption in liters per $100\ \text{km}$ per passenger.

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.

An electricity bill has two parts: a fixed standing charge for power of $\$24$ 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 home consumes $4200\ \text{kWh}$ per year, while the average consumption of Mexican 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 pesos (at $3.40\ \text{\$/kWh}$) would be saved per year?

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 $c_e = 4180\ \text{J/(kg}\times^\circ\text{C)}$.

1. a) Calculate the energy of one shower using $Q = m\times c_e\times\Delta T$ and express it in $\text{kWh}$, rounding to one decimal place (remember: $1\ \text{kWh} = 3.6\times10^{6}\ \text{J}$).
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 liter of fuel is equivalent to $9.5\ \text{kWh}$):

• Gas 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 trip, with $200$ passengers.

The diagram summarizes the data for the three options:

1. a) Calculate the total energy of the trip 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 traveled in it? Justify your answer with the calculation.

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 gas car consumes $6.5\ \text{L}$ per $100\ \text{km}$ and an equivalent electric car consumes $16\ \text{kWh}$ per $100\ \text{km}$. Note: each liter of gas contains about $9.5\ \text{kWh}$ of energy.

1. a) Express the consumption of the gas car in $\text{kWh}$ per $100\ \text{km}$.
2. b) How many times more energy does the gas car use than the electric one on that trip? Round to one decimal place. Explain what accounts for such a large difference, given that an internal combustion engine loses about two thirds of the fuel's energy as heat.
3. c) Calculate the cost of each per $100\ \text{km}$ if gas costs $31\ \text{\$/L}$ and electricity costs $3\ \text{\$/kWh}$.

A country house is heated by a natural gas boiler that consumes $900\ \text{m}^3$ of gas per year. Each $\text{m}^3$ of gas provides $10.5\ \text{kWh}$ of energy, but the boiler has an efficiency of only $90\ \%$.

1. a) How many $\text{kWh}$ of chemical energy does it consume per year?
2. b) How many $\text{kWh}$ of useful heat actually reach the house?
3. c) Switching to a heat pump with $\text{COP} = 3$ is considered, meaning that for every electrical $\text{kWh}$ it consumes, it delivers $3\ \text{kWh}$ of heat. How many electrical $\text{kWh}$ would it need to deliver the same useful heat?
4. d) Compare the annual cost of both options if gas costs $1.20\ \text{\$/kWh}$ and electricity costs $3\ \text{\$/kWh}$.

A family has a time-of-use electricity tariff: energy during off-peak hours costs $2\ \text{\$/kWh}$ and during peak hours $4.40\ \text{\$/kWh}$. 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.

On a flight, each passenger consumes about $2.5\ \text{L}$ of fuel per $100\ \text{km}$. A flight of $1800\ \text{km}$ connects two cities. Note: each liter of fuel is equivalent to $9.5\ \text{kWh}$.

1. a) How many liters does each passenger consume on that flight?
2. b) Express the energy of that consumption in $\text{kWh}$.
3. c) Compare it with the annual electricity consumption of a household, $3600\ \text{kWh}$: what percentage does a single flight per passenger represent? Comment on the result.