Understanding Watt vs. Kilowatt-Hour: A Comprehensive Explanation

[kuin]

Hello,

getting confused about watt vs watt.hour

in the Watt's wiki page, an example is given on how to calculate wattage (power):

A person having a mass of 100 kilograms who climbs a 3 meter high ladder in 5 seconds is doing work at a rate of about 600 watts. Mass times acceleration due to gravity times height divided by the time it takes to lift the object to the given height gives the rate of doing work or power

So, (100kg x (9.81m/s²) x 3m) / 5s = 588 kg.m²/s³

this system needs aroud 600 watts of power to accomplish its task. ok.

Then, lower in the page, an example is given on how to calculate watt.hour(energy):

For example, when a light bulb with a power rating of 100W is turned on for one hour, the energy used is 100 watt-hours (W•h), 0.1 kilowatt-hour

Now, if I go back to my first example, it's being done in 5 seconds for 588,6 watts

if it was done in 1 second, it would be 2943 watts

if it was done in 3600 seconds, it would be 0,8175 watts

So, if I do the work on a 1 hour (3600 sec) time span, can say I use 0,8175 watt.hour?

And if I lift the thing in 1 second, but constantly, for 1 hour, do I use 2943 watt.hour?

This is confusing me a little, so I guess my question also is a little confused. I looked many places where it was promised that this confusion would evaporate after reading their explanations. Now I'm here because I'm still a little lost.

thanks

 

[sophiecentaur]

It may help to ignore the actual figures for a start. The Watt is a unit of Power - the rate of doing work or using energy. The kW hour is a unit of Energy - just like the more basic Joule. If you read each problem / example carefully you will always see whether Power or Energy is what is needed.
Power is Energy / Time
Energy is Power X Time
Hold that in your head and the numbers will look after themselves.

 

[russ_watters]

This is confusing me a little, so I guess my question also is a little confused. I looked many places where it was promised that this confusion would evaporate after reading their explanations. Now I'm here because I'm still a little lost.

thanks

Welcome to PF!

Your confusion isn't affecting your ability to do the math, so I'm not sure what there is we can do to help other than to tell you to trust your understanding, because you understand correctly.

...Or ask us another question...

 

[ParamTv]

NO need to confuse over it. Just Take it easy. I try to make it clear.
Actually the rate of work done is called power. I mean for calculating the power you must know the work done. ... Work done per sec is called power and measured in Watt. Work done per minute is also power. Work done per hour is also power but measured in Watt.hour.
Actually Watthour And killowatthour is represent the power produce by a machine in 1 hour.

Suppose a machine produce 1500watt power in one sec. then it will produce 1500X60 watt in a minute and 1500x60x60 in a hour or i can say 1500x60x60/100 Kwatthour (KWH)
hope you understand
thanks

 

[sophiecentaur]

Yep. Two issues here. 1. Believe the Physics. 2. Believe the arithmetic.

 

[russ_watters]

Yep. Two issues here. 1. Believe the Physics. 2. Believe the arithmetic.

3. Believe the [mathematical] definition of the words.

 

[nasu]

NO need to confuse over it. Just Take it easy. I try to make it clear.

Actually Watthour And killowatthour is represent the power produce by a machine in 1 hour.

No, they represent energy and not power.
A watt-hour represents a specific amount of energy (3600 J) no matter in what time is this energy used or transformed.
Even saying "power produced in 1 hour" is meaningless.
The machine "produces" energy. Power shows you how fast is done, not necessarily how much of it.
1 watt -hour of energy may be "produced" in 1 second or 1 billion years. It's still 1watt-hour.

 

[sophiecentaur]

No, they represent energy and not power.
A watt-hour represents a specific amount of energy (3600 J) no matter in what time is this energy used or transformed.
Even saying "power produced in 1 hour" is meaningless.
The machine "produces" energy. Power shows you how fast is done, not necessarily how much of it.
1 watt -hour of energy may be "produced" in 1 second or 1 billion years. It's still 1watt-hour.

I agree.
I find people's determination to use the wrong terms, in this way, very annoying. It's as if they really don't get it. People who get aerated about the 'offside rule', as if it's actually important. But they will use scientific terms interchangeably like some poet who can't bring himself to use the same word twice in a sentence and scrabbles around to find a shoddy equivalent. The fact is that there is, with very few exceptions, only one word for each scientific concept. It just does not help anyone to have the alternative (wrong) terms used instead. It doesn't make the subject any more approachable - just the reverse.

I heard some clown of an energy minister on BBC Radio, recently, talking about "storing Power"! What hope do we have?

 

[nasu]

I heard some clown of an energy minister on BBC Radio, recently, talking about "storing Power"! What hope do we have?

Well, for a minister I think it's OK. He's not trying to learn or teach (thanks God) physics.
In common language, power is used so often for "energy" that maybe you should close you eyes. It's a "power station" or "power plant" after all. At least in North America.
A car factory produces cars which are stored in parking lots. So what does a power plant produce (and store)?

 

[sophiecentaur]

I clearly made the mistake of hoping that he should know what he's talking about.
If he's as ignorant as that, how can he distinguish between sense and nonsense when he's being sold some idea by a flash salesman? The distinction could be highly relevant to making a good decision.
For instance, what use is a 5MW wind turbine if it only operates for 30 days per year?
(You wouldn't be confused, by common language, yourself would you? )

 

[K^2]

For instance, what use is a 5MW wind turbine if it only operates for 30 days per year?

Sell excess back to electric company in these 30 days, use power from the grid for the remaining 335 days. At 5MW, you are still going to be making a net profit.

:p

 

[nasu]

For instance, what use is a 5MW wind turbine if it only operates for 30 days per year?
(You wouldn't be confused, by common language, yourself would you? )

Oh, I did not pay attention that you said energy minister.
This makes some difference.

 

[nasu]

Sell excess back to electric company in these 30 days, use power from the grid for the remaining 335 days. At 5MW, you are still going to be making a net profit.

:p

And how is the electric company going to store all the power it buys from people?

 

[sophiecentaur]

Oh, I did not pay attention that you said energy minister.
This makes some difference.

Well, that's what he calls himself. It can't be 'Minister of Power'; the PM wouldn't like that.

 

[sophiecentaur]

Sell excess back to electric company in these 30 days, use power from the grid for the remaining 335 days. At 5MW, you are still going to be making a net profit.

:p

Hmmm
Not sure you could actually fit a 5MW turbine on your roof. I was thinking more of those big devils out at sea. They are owned and run by the Elec company.

Did you consider the capital cost of one that big?

 

[the_emi_guy]

Kuin,

Here is an analogy for you.

The bottled water factory produces 8,000 gallons per day.

I can store 10 gallons in my pantry.

See the difference between "gallons per day" and "gallons"?

 

[sophiecentaur]

Nasu,

Here is an analogy for you.

The bottled water factory produces 8,000 gallons per day.

I can store 10 gallons in my pantry.

See the difference between "gallons per day" and "gallons"?

If that's beer then we can have a party.

 

[CWatters]

A lot of the confusion comes because the energy companies use kWh as a measure of energy which it is (because its power * time) but it's not a basic unit like the joule. To make matters worse you sometimes find people talking about "kWh per hour" which is the same as saying kW.

 

[sophiecentaur]

Same quantity but one is time averaged (e.g. including a thermostat operating) and the other is instantaneous. That first one may look hideous but it could have relevance somewhere.

 

[kuin]

ok, thanks for all the replies, I think I got a glimpse at something, the fog seems to be thinning out.

So, is my understandng right if say :

I attach a mass of 102 grams (0,102 kg) to a 1 meter long string that is wound around a shaft that turns a small electric generator. (assume a perfect no loss system)

When I let the weight go down, it would ''produce'' a power of 1 Watt, or 1 Joule per second.

because 0,102kg\times\frac{9,81m}{1s^{2}}\times1m / 1s = 1 Watt.

BUT, this works only if the duration is exactly 1 second. How do I make this happen? If I get around the problem and say I lift the thing in 1 second, now it's easy, I control that, but if I have to let gravity do the work, how can you control the duration?

Then for watt-hour:

Say I have a very very long string and the generator is up the highest cliff. I let the 102g mass go down for 1 hour. Will it produce 1 watt-hour of energy?

thanks

 

[the_emi_guy]

nasu,
Sorry, I mis-directed my last post at you. Sorry, I have updated it.

Kuin,
I think you have it, your calculations look correct.

You ask how would you control your gravity-weight-generator mechanism in order to have it produce at a steady rate of 1Watt? This would require some kind of speed regulator, the generator would have to be spinning at a constant rate.

The real question is, why would you want/need to do this? In reality, the weight would eventually reach a terminal velocity where the reaction force from the spinning generator was equal to mg, but prior to this, the output rate in watts would not be constant.

In other words, power is, or can be, a function of time in which case finding total energy would require integrating over time vs. multiplying by time.

 

[nasu]

Then for watt-hour:

Say I have a very very long string and the generator is up the highest cliff. I let the 102g mass go down for 1 hour. Will it produce 1 watt-hour of energy?

thanks

You are still going around in circles.
1 watt-hour is 3600 J.
The weight of your mass is about 1 N. It has to go down 3600 m for the work of gravity to be 3600J or 1W-hour. No matter how long it takes. Work= F*d See? no time in here!
How fast it goes down determines the power (in watt) and not the energy in Watt-hour.

 

[TheAbsoluTurk]

1 joule is equal to 1 watt second. (Ws)

Does that help? I didn't bother to read all responses yet.

 

[kuin]

So,

in the end, what I'm trying to do is to find a way to get a clear image of the energy used by a typical household over the course of 1 year. A north american typical household of 4 people uses around 10 000kwh every year.

but it's hard to figure out what that means so I'm trying to convert that to something we can understand instinctively. I think weights moving up or down give the clearest 'picture' for that purpose. So I'm trying to figure out what 'size' of a weight would have to travel how high to 'work' 10 000kwh.

As for the weight itself, water is a good pick, people can easily imagine what a liter of water 'feels' like, and it is also handy since 1 liter of water has a weight of 1kg.

so, is this right:

10 000kwh = 36 000 000 000 N-m = 3 670 978 356 kg-m

so, 3 670 978 356 kg going down 1 meter would produce 10 000 kwh

or 36 709 783 kg going down 100 meters

so we need to picture a cube of water containing 36 709 783 liters of water going down 100 meter.

cubic root of 36 709 783 is 332 liters(10cmx10cm,x10cm) of edge for the cube, that is

332 x 10cm = 3323cm = 33meters

So a cube 33 meters of side, filled with water, going down 100 meters represents the energy usage of 1 north american household... 33 meters is about the height of a 10 story building. 100 meters would be a 30 story building.

I must be wrong, this would be crazy! this seems a lot.

is this right?

 

[gmax137]

...

I must be wrong, this would be crazy! this seems a lot.

is this right?

Yes, I think you're right -- I get the same answer. It isn't crazy, it's just that gravity isn't very strong. Big hydroelectric dams need rivers with a lot of flow and a lot of head.

 

[sophiecentaur]

Mechanical Work involves very little energy compared with heating things up, in general. We seem not to weight them the same in our appreciation. A 1kW heater would not make a lot of difference to a house if run for an hour. A 1kW power tool could make a very significant difference in the same time.

 

[nasu]

So,
in the end, what I'm trying to do is to find a way to get a clear image of the energy used by a typical household over the course of 1 year. A north american typical household of 4 people uses around 10 000kwh every year.

I think the figure is reasonable.
We use an average 500kwh per month so it will be 6000 kwh per year. But it's a small house.

However very little of this is used to move things around.
I would say that at least 1/2 if not more is used to heat up things around, mostly water.
Why not take sophiecentaur's hint and estimate how much water can be heated up from room temperature to around 70-80 degrees, by using this energy?. It would give you a more meaningful image.

With the energy equivalent of the heat required to bring the water in your coffee cup to boiling point you can lift the same water some 30 km.
Did you ever worried in the morning about how "huge" is this?

 

[sophiecentaur]

When I was at School, they taught us about the work of Joule. He came up with the concept of 'The Mechanical Equivalent of Heat', based on the heating effect of boring through the barrel of a gun and other such activities. I don't think Energy was seen in quite the same light at the time (Joule's day - no my school days) and the Joule (Work) was measured as equivlent to 4.2 Calories (Heat). This was when they finally realized that the old 'Caloric' theory of heat was nonsense and that heat could not just be treated as a fluid that flowed from place to place.
The calorie is such a small amount of heat that they went and confused everyone by introducing the kiloCalorie - which was then referred to as the Calorie, in the context of Food energy content. That factor of a thousand can often get lost in arguments about eating and exercise.

 

[kuin]

Why not take sophiecentaur's hint and estimate how much water can be heated up from room temperature to around 70-80 degrees, by using this energy?. It would give you a more meaningful image.

I will, the more the better. But I will also stick to my idea, the reason being that for someone to imagine lifting a weight is possible, but to imagine producing heat is very difficult to do meaningfuly, with real accurate data to support the example.

You have the example of rubbing your hands together, but it's hard to get any precise idea of the amount of energy input and of heat output.

Thanks again to everyone.

 

[sophiecentaur]

I will, the more the better. But I will also stick to my idea, the reason being that for someone to imagine lifting a weight is possible, but to imagine producing heat is very difficult to do meaningfuly, with real accurate data to support the example.

You have the example of rubbing your hands together, but it's hard to get any precise idea of the amount of energy input and of heat output.

Thanks again to everyone.

I just can't understand that remark at all. What about the way an electrical generator converts mechanical energy to electrical power for heating homes? It's all going on, every day, in front of your nose and there is so much information about it all. You can say exactly how much heat energy is needed to warm up a given amount of water by a certain temperature. You have shedloads of statistics about home energy consumption available. What more could you want? What exactly are you hoping to achieve? Is it just that you want to get familiar with the numbers involved?
If you are interested in experiments on converting mechanical energy to heat then there is much info about Joule's early work. It is worth doing the calculations around his experiment on temperature changes as water fell down a waterfall and it is very easy to work out the theoretical rise in temperature you would expect if all the Gravitational Potential Energy went into heating the water at the bottom. It certainly brings home the 'difference' between the two aspects of Energy.