Question

Question #32d48

Answer 1

To go from Joules to kWh you just have to use a simple conversion factor

`3.86 * 10^(10)cancel("J") * (2.77778 * 10^(-7)"kWh")/(1cancel("Joule")) = 1.0722 * 10^(4)"kWh"`

Rounded to three sig figs, the answer will be `1.07 * 10^(4)"kWh"`.

Answer 2

I believe it's appropriate to explain the reasons behind the calculations presented in the first answer.

Let's start from definitions.

Joule (abbreviated as `J`) is a unit of energy equal to work made by a force of 1 newton (`1N`) at a distance of 1 meter (`1m`):
`1J=1N*1m`

Watt (abbreviated as `W`) is a unit of power (that is, energy per unit of time) equal to work of `1` Joule (`1J`) per second (`1sec`), that is `1W=(1J)/(1sec)`.

Therefore,
`1W*1sec=1J`
or, in words, one Joule equals to one Watt-second.

Now we have to transform watt and second into kilowatt (`1kW=1000W`) and hour (`1h=3600sec`):
`1kWh=1000W*3600sec=3600000J`

Or, reversing this equality,
`1J=1/3600000kWh=2.777778*10^-7kWh`

Using the above equality, we do the calculations presented in the first answer:
`3.86*10^10J=(3.86*10^10)/3600000kWh=`
`=(3.86*10^10)/(3.6*10^6)kWh=1.0722*10^4kWh`

As you see, all the difficulties of this problem lie in the definitions of the units of measurement: the two main ones (`1J=1N*1m` - unit of energy and `1W=(1J)/(1sec)` - unit of power) and a derived unit of kilowatt-hour, which is a power of `1000` watt applied during the time of `1` hour.