Question #32d48

2 Answers
Mar 21, 2015

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"#.

Mar 21, 2015

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.