What is 7.8 kilowatt-hours in joules?
Now in this question, we’ve been asked to convert from kilowatt-hours to joules, both of which are units of energy. Let’s start by considering a kilowatt-hour. One kilowatt-hour is the same as one kilowatt multiplied by one hour, hence it’s called a kilowatt-hour. Also, the reason that a kilowatt hour is a unit of energy is the following: on the left-hand side we have a kilowatt-hour; and on the right- hand side, we’ve got a kilowatt, which is a unit of power, multiplied by an hour, which is a unit of time.
Now if we consider the definition of power, then power is the energy transferred per unit time. So if we rearrange the equation by multiplying both sides of the equation by the time 𝑡, we find that on the right-hand side the times cancel out. And so we’re left with time multiplied by power is equal to energy. Now time multiplied by power is the same as power multiplied by time, and hence one kilowatt multiplied by one hour is the same as a unit of power multiplied by a unit of time.
Anyway, coming back to the question then, firstly what is a kilowatt? Well the prefix kilo- means 1000. So a kilo watt is the same as 100 watts. So that’s what a kilowatt is. But what is an hour in standard units? Well the standard unit of time is the second. So we need to convert one hour into seconds. Now we know in one hour there are 60 minutes; and in every minute, there are 60 seconds. So in one hour, there are 60 times 60 seconds.
And this is the same as 3600 seconds. So in standard units, one kilowatt-hour is the same as 1000 watts times 3600 seconds. If we multiply these two together, the number we get is 3600000 and the unit is watt multiplied by seconds, watt- seconds. But remember, we saw earlier that the units of energy were the same as the units of power multiplied by the units of time.
Well. the standard unit of energy is a joule. The standard unit of power is the watt. And the standard unit of time is the second. Hence, one joule is equal to one watt multiplied by one second, or one joule is equal to one watt- second. So when we see watt-seconds, we can convert them into joules. And since one watt- second is the same as one joule, we simply replace watt-seconds with joules, at which point we’ve converted one kilowatt-hour into joules; that’s 3600000 joules.
However, this is not our final answer because we’ve been asked in the question to convert 7.8 kilowatt-hours into joules. To do this, we simply multiply both sides of the equation by 7.8, which on the left-hand side gives us 7.8 times one kilowatt-hours, so that’s 7.8 kilowatt hours. And on the right-hand side, we’ve got 3600000 multiplied by 7.8 joules. When we evaluate the right- hand side, we find that 7.8 kilowatt-hours ends up being 28080000 joules. And hence we found our final answer: 7.8 kilowatt-hours in joules is 28080000.