# KW and kWh - further explanation

1. Jan 23, 2014

### danny.mcshane

I have been looking at the difference and I know one is power and one is energy. I understand that a 2kW kettle on for an hour uses 2kWh but on for 30 minutes uses 1kWh. But with power generation it seems this is constant. If a plant puts out 100kW it does this all day every day regardless of time. What I have read says time cannot be applied but how does it work?

Does that power stack at all??? I'll do an example to show what I mean.

So I am selling EDF and I am selling energy. At 8.00.00am in the morning my plant was producing 100kW and there were 50 kettles on so all my energy was sold. at 8.00.01am I am producing 100kW, the 50 kettles are sill on so I sell another 100kW. Carry this on assuming there was demand for all my power and in the whole hour my 100kW power station has sold 360,000kW of energy.

I instinctively know this is wrong but cannot figure out why.

2. Jan 23, 2014

### Brinx

In 1 second, you're selling 100 kW * 1 s = 100 'kWs' = 100 kJ. Expressed alternatively, this is about 0.028 kWh because 1 kWh = 1000 W * 1 h = 1000 W * 3600 s = 3.6 * 10^6 J.

In the whole hour, you have sold 100 kW * 3600 s = 3.6 * 10^8 J = 100 kWh.

Power integrated over time equals energy.

3. Jan 23, 2014

### danny.mcshane

So when they say a the new nuclear station will be a 4.2GW station, they are really saying it will be a 4.2GWh station as well.

4. Jan 23, 2014

### Staff: Mentor

No. That would be the amount of energy produced by the station in one hour. Multiply by 24 to get the amount of energy produced in a day.

5. Jan 23, 2014

### QuantumPion

It is 4.2 GWh per hour.

6. Jan 23, 2014

### SteamKing

Staff Emeritus
The thing about power stations is that they can adjust their power output to meet the local electrical demand. On hot days, when there are a lot of air conditioners in use, the local power plant will be cranking along at full output. On a spring day or a fall day, when the temps. are more moderate, the power plant cuts back its output.

Now, power plants are usually built to serve part of a city or a local region. In order to provide flexibility in times of high demand, power plants from far away to one locale are linked to the electrical grid, which allows the transfer of electricity from a region with a low power demand to a region with a higher demand.

7. Jan 23, 2014

### nschaefe

Energy = a quantity/ amount of something. Power = the rate at which you use that energy. For example, replace the idea of energy with water. If your toilet uses 5 gallons of water per flush, this would be analgous to it using 5 "gallons" of energy. But now look at your sink. Obviously, if you turn the sink on, how do you measure how much water (energy) you are using? Because the longer you leave your sink on, the more water (energy) that flows down the drain. Thus, it doesn't make sense to talk about a sink in terms of how many gallons of water it uses, because it would depend on how long the sink was left on. However, you can express the sinks water usage as a flowrate (power). You could say, the sink uses 5 gallons of water per minute. Then, if you knew how long the sink was left on, you would know how much water ended up flowing down the drain.

Going back to energy, Joules are units of energy, and 1 Joule / 1 second = 1 Watt

This is analogous to electricity. Consider an appliance, like your refrigerator, which is constantly running. How can you express the amount of energy your fridge has used? Without the context of time, you can't. Instead, you say, my fridge uses 1000 Joules of energy every second, in other words my fridge consumes 1 kW of power. Or you could say, my fridge uses 100,000 Joules of energy every 10 seconds = 1 kW of power.

Now look at the units of a kWh -> (Joules/second)*(hour) = (Joules/second)*(3600 seconds) = 3600 Joules. In other words, a kWh is really just a clever way expressing an amount of energy. Going back to my fridge, if my fridge is rated for 1 kW of power consumption, and I run it for 1 hour, then I can say my fridge has used 1 kWh of energy = 3600 Joules.

So why doesn't it make sense to add the power your station has output over an amount of time? Well, if you sold water towers and your water towers had a flowrate of 100 gallons / sec (kW), then you can see it makes no sense to say my water tower sold 360,000 gallons / sec of water over an hour. However, you can say your water tower has sold 360,000 gallons of water, or 100 (gallons/sec)*hour (kWh)

Hope this makes sense

8. Jan 23, 2014

### danny.mcshane

OK so is it 100kW every single hour. So over a day it produces 2400kW. Is that right? The new Nuclear power station will make a fortune. Why does the government need to subsidise it????

9. Jan 23, 2014

### QuantumPion

If it generates a constant 100 kW, it will produce 100 kW*hr/hr or 2400 kW*hr/day.

If your car goes 50 mph, then after one hour you will travel 50 miles and after one day you will travel 1200 miles.

The reason why the government is subsidizing nuclear power plant construction is because the plant will cost somewhere around \$10 billion to build and will take maybe 5 years to complete. Not many companies can afford to tie up that much capital for that much time while paying interest on it to boot.

Last edited: Jan 23, 2014
10. Jan 23, 2014

### Staff: Mentor

100kW * 1h = 100kWh.

100kW * 24h = 2400kWh.

11. Jan 23, 2014

### sophiecentaur

@danny.mcshane
I'm sure you would never have this problem if you had a discussion about car journeys. You would instantly realise that mph is not the same as miles and where each quantity was appropriate. Also, if someone talked about miles per second, you would catch on immediately to what they meant.
It's just the same with Joules and Watts etc. etc..

12. Jan 23, 2014

### SteamKing

Staff Emeritus
When you get your electric bill, they usually tell you how many KWh you used in a month and what rate per KWh the utility company is charging you. You can take the electric appliances in your house and figure out how much it costs you to run each one every month.

Constructing a nuclear plant is a huge undertaking. In addition to satisfying all of the regulatory requirements, the construction provides hundreds of jobs for several years. Local governments like to be involved with these types of projects, especially around election time.

13. Jan 24, 2014

### danny.mcshane

Thanks guys, as always I am really appreciative of the help and suitably embarrassed by the simplicity of the answers. I am sticking at it though, physics is fascinating. Someday I would like to answer a question on the forums. On that day I will be a very happy man.