Horsepower to kilowatt-hours?

[rolodexx]

SOLVED - Horsepower to kilowatt-hours?

Homework Statement

In the English system of units, power is expressed as horsepower (hp) instead of watts, where 1 hp=746 W. Horsepower is often used for motors and automobiles.
How many kilowatt-hours of energy is produced when you run a 23.0 hp motor for 240 minutes?

Homework Equations

1 hp=746 W
1000 W=1 kW
60 min = 1 hr
60 s = 1 min
1 W = 1 J/s

The Attempt at a Solution

I started by converting horsepower to Watts, then dividing by 1000 to get kilowatts. I then multipled by 3600 (60*60) to convert to kWs to kWh. I am then left with 4 hr (240 min) to factor in somewhere, but I don't know how to relate it to kWh with all the conversions happening. I tried multiplying by 4 but it said it was wrong.

 

[chroot]

Do you know how to use dimensional analysis?

- Warren

 

[blochwave]

Remember that power times time is energy

You're given a power, and you're given a time.

Unfortunately, if you multiply them together you get the somewhat useless unit of hp*minutes, when you really wanted kW*hrs

 

[rolodexx]

What is dimensional analysis?

Also, I already considered that I needed hours, so since a Watt is a unit in seconds I multipled by 60 s/min and 60 min/hr to get the right time unit... and I divided the Watt term by 1000 because of how my equation was set up.

 

[blochwave]

dimensional analysis is basically what you're doing, analyzing units

The two simplest ways to do this is just multiply 23*240, and then convert horsepower-minutes to kilowatt-hours, or convert 23 hp to watts and 240 minutes to hours, and multiply(and those two ways are really the same thing, you're just combining two steps into one or not)

Let's see what you did, you took a value in watts, a J/s in other words, and turned it into...a kJ/hr? A kJ/hr is still a unit of power(energy/time)so now assuming you did the conversions right you could convert 240 minutes into hours and multiply to get the answer in kJ

then convert kJ to kW-hrs. So yah you could finish it the way you started, but you'll notice your first steps didn't really help you, and in fact just made it longer

 

[rolodexx]

If kJ is a unit of energy, how do I get it back to power when I already used up the time portion of the unit by multiplying by 4 hr?

 

[rolodexx]

hmm, I got it... lucky break, I guess. I found a unit conversion somewhere online that listed 1 kWh as 3.6 * 10$$^{6}$$ J... so I used what I had made in kJ and changed it back to J, and divided it by the 10$$^{6}$$ conversion, and it was right! But I still don't understand how the assumption of power came back even though I got rid of the time...

 

[blochwave]

Well you sort of confused yourself with what you were doing

Remember, ANY unit of energy in all of heaven and earth, be it joule, erg, BTU, or whatever, divided by ANY unit of time is a unit of power. We just happen to have a special name for 1 joule / second, we call it a watt

On the flip side, ANY unit of power blah blah times ANY unit of time is a unit of energy. So 1 watt-second is a joule!(1 watt*second=1 J/s*s=1 J), specifically it's the total amount of energy if you had that power for that amount of time(so if you ran something at 1 watt for 1 second, it'd give you 1 joule of energy)

So you started in horsepower, a unit of power and changed it to watts, also a unit of power

A watt is a J/s, when you divided by 1000 you got it in units of kilowatts, or kJ per second, then when you multipled by 3600, you changed it from kJ/sec to kJ/hour

kJ/hour is STILL a unit of power, it's energy/time. THEN you multiply by 4 hours and you have the energy produced by that power in 4 hours, which is just in kJ. Then you needed to convert kJ to kW-hr(which is power times time, hence energy!

if 1 watt-second=1 joules, then 1 kW-sec=1000 joules, so 1kW-hr=1000*3600 joules!

 

[rolodexx]

Thanks for the help! I can tell getting this is going to take some practice...

 

[chroot]

blochwave is making a disgusting mess of this. Please don't take him too literally, for he's making this way more difficult on you than necessary. He's making a number of grave mistakes, like using numbers without units, converting to seconds unecessarily, etc.

Instead of thinking about units, think about conversion factors. Conversion factors are nothing more than fractions. When you multiply fractions, you can cancel things that are common on the top and bottom. We're going to use this same powerful concept to do unit conversions.

I'm going to cast your example in fractions:

$\left( 23.0\,hp \cdot \frac{ 746\,W }{ 1\,hp } \cdot \frac{ 1\,kW }{ 1000\,W } \right) \cdot \left( 240\,minutes \cdot\frac{ 1\,hour }{ 60\,minutes } \right)$

In each set of parentheses, I have taken the quantities you were originally given (23 hp and 240 minutes) and written them down directly. Next, I multiplied by a number of conversion factors. Note that each conversion factor (like 746 W / 1 hp) is effectively equal to one, since the top and bottom are equal quantities, just represented in different units.

I have applied two conversion factors on the left to get from hp to kW. I have applied only one on the right to get from minutes to hours.

Now, notice that all the units cancel on the left, except the kW. All the units cancel on the right, except hours. You're thus left with this:

$\frac{ 23.0 \cdot 746 }{ 1000 }\,kW \cdot \frac{240}{60}\, hours$

You can type these simple expressions into your calculator, giving you this:

$17.158\,kW \cdot 4\,hours$

And obviously it's pretty simple to multiply those and get kW-hours. I recommend that you really think very carefully about each of these steps, and try some other examples on your own. This technique is called "dimensional analysis," and it's one of the simplest and most useful techniques you'll ever learn. You'll find yourself using it all the time.

- Warren

 

[blochwave]

Whoa there cowboy, admin or not, you know no self respecting man can take that shot sitting down! The only place in the two posts where I'll concede I should have been more obvious was stating 23*240, but then I immediately stated what units they were in, so I won't accept that as a disgusting mess.

Then I told him to do exactly what you explicitly did for him, I had assumed for at least the first post that he was proficient at converting units(even if he didn't know the official title of the process) since he apparently had no trouble going from horsepower to watts and watts to kilowatts, or 240 minutes to 4 hours. The rest of the post I explained why what he had begun doing, besides him not fully understanding it, was way more complicated and, I daresay, a mess.

I rather like the first part of my second post, and then the rest was the same, explaining what was actually happening with his haphazard multiplication. Had he come back with something besides "thanks", I would've gone into more detail.

He's making a number of grave mistakes, like using numbers without units, converting to seconds unecessarily, etc.

? That's not even true! Pistols, noon, 10 paces, etc. Seriously though, compulsive need to prove myself in front of authority figures, plus I'm reasonably certain you skimmed my posts and missed

Let's see what you did

Edit + sad admission - I did have one typo style mishap but I already fixed it and I don't think you noticed since you resorted to making up mistakes before mentioning it! Can we scoot the duel to midday, I'm full that morning

 

[stevegyro]

oops. I see Warren already "nailed it".

 

[ideasrule]

Can we scoot the duel to midday, I'm full that morning

Do you really want to take on somebody called chroot? He'll ch more than your root!

 

[darkmagic]

1 kilowatt-hour = 3.6 megajoules = work
power = work / time

 

[Tatersoup]

Although many have the correct answer, Chroot is the one who is correct on both the problem as well as the methods.

If this problem were before a trial jury due to some engineering error, good luck with any methodology other than Choot's. This method not only solves the problem, but also makes the answer so clear as to forego any scrutiny, as long as the answer is correct. Any of the other methods would lead an adverse attourney to attack relentlessly and will probably trip up the testifier enough to confuse a jury to believe that the answer might indeed not be right.

 

[stein21]

240 minutes is 4 hours therefore 23 horsepower x 4 hours is 92 horsepower-hours
1 kw-hr = 1.34 hp-hrs

therefore the number of kw-hrs is 92/1.34 = 68.6 kw-hrs

 

[JeffB]

There is no such thing as a 23 hp motor
They come in standard sizes 20 hp 25 hp etc.