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# Energy in the home

## In a nutshell

Every time you use an electrical appliance in your home, energy will be used and charged for by an energy company. Energy companies measure energy in kilowatt hours ($kWh$) and charge a rate per $kWh$. The more power an appliance needs, the more energy will be used.

**Equations**

#### Word Equation | #### Symbol Equation |

$energy \space transferred = power \times time$ | $E = P \times t$ |

$total \space cost = energy \space in \space kWh \times cost \space per \space kWh$ | |

**Variable definitions**

#### Quantity Name | #### Symbol | #### Unit Name | #### Unit |

$energy \space transferred$ | $E$ | $joule$ | $J$ |

$power$ | $P$ | $watt$ | $W$ |

$time$ | $t$ | $second$ | $s$ |

## Power and energy transferred

Power is the rate that energy is transferred. The higher the power rating of an appliance, the more energy is transferred in a given time.

For example, a $3000 \, W$ kettle will transfer energy quicker than a $2000 \,W$ kettle.

You can calculate power using the following equation.

$energy \space transferred = power \times time \\ \ \\ E = P \times t$

##### Example

*A kettle takes $2 \, minutes$ and $5 \, seconds$ to boil half a litre of water and requires $165\, kJ$of energy to do this. What is the power of the kettle?*

*Firstly, you need to convert $165 \,kJ$ into joules:*

*$1 \space kJ = 1000 \space kJ$*

*$165 \space kJ = 165000 \space J$*

*Next, you need to convert the time into seconds:*

*$1\space minute = 60 \space seconds$*

*$2 \space minutes + 5 \space seconds = 125 \space seconds$*

*Now, rearrange the equation:*

*$power = energy \div time$*

*Substitute the values into the equation:*

$P = 165000 \div 125$

*Don't forget your units!*

*$1320 \space W$*

*The power of the kettle is $\underline{1320\,W}$.*

## Energy bills

### Kilowatt hours ($kWh$)

Energy companies measure energy in kilowatt hours ($kWh$) and charge you for how much energy you have used in your home. To convert energy into $kWh$ you need to use the following equation.

$energy \space transferred\space in \space kWh = power \space in \space kW \times time \space in \space h$

*Hint*: $1 \, kW$* is $1000 \, W$.*

##### Example

*The power of a fridge freezer is $175 \, W$. How much energy is transferred in $kWh$ in an hour?*

*Firstly, convert power into kilowatts:*

$1000 \space W = 1 \space kW \\ \ \\ 175 \space W = 0.175 \space kW$

*Next, substitute into the equation:*

$energy \space transferred = 0.175 \space kW \times 1\space h$

*Don't forget your units!*

$0.175 \space kWh$

*The fridge freezer transfers $\underline{0.175 \, kWh}$ in one hour.*

### Calculating energy bills

Energy companies will then charge a price per $kWh$. To work out the total cost of energy, you need to multiply the cost of a $kWh$ and energy in $kWh$ used.

$total \space cost = energy \space in \space kWh \times cost \space per \space kWh$

##### Example

*An energy company charges $10 \, p$ per $kWh$. A household uses $500 \, kWh$. How much will the energy bill be in pounds?*

*Firstly, substitute values into the equation:*

$total \space cost = 500 \space kWh \times 10 \space p$**

*The total cost in pence is:*

$5000 \space p$**

*Convert from pence to pounds by dividing by $100$:*

$£ \,50$**

*The total cost of the energy bill will be $\underline{£ \, 50}$**.*

## Energy in food

Chemical energy stores in food transfers chemical energy in your body when you eat. On food packages, there are labels which tells you how much energy is in food. This is normally in kilocalories ($kcal$). $1 \, kcal$ is equivalent to $4184 \, J$ of energy.