Homework Help/Check

rtparty

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So my wife is taking an Urban Ecology class and we've run into a problem that the answer seems crazy to. It is pretty simple math but the answer is astronomical. Hoping someone on can check our work or at least help us out..

The question states: How much wood do you need to burn to run the human body at 100w or 2.4kWh per day given the energy density of wood is 0.02kJ/kg?

Our math is this:

1kWh = 3600kJ

2.4kWh x 3600kJ = 8,640kJ/day

8,640kJ/.02kJ/kg = 432,000kg/day


Does any of this make sense? Is the formula correct? That seems like a ton of wood to run the human body.

Thanks in advance if anyone understands this stuff. It's over my pay grade
 

MWard

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That math looks like it checks out?
 

rtparty

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That math looks like it checks out?
I like the question mark. That is how we feel as well. Are we sure that looks right???
 

arydolphin

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100 Watts = 100 Joules/second. In a day, that's 100 Joules/second X 86400 seconds/day = 8640000 Joules/day.

0.02 kJ/kg = 20 Joules/kg. So 8640000 Joules/day divided by 20 Joules/kg = 432000 kg/day.

Different way to do the math, but the result is the same.
 

MWard

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I like the question mark. That is how we feel as well. Are we sure that looks right???
Yeah when you see numbers that big you have to raise an eyebrow to it. That's a ton of energy!
 

rtparty

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Yeah when you see numbers that big you have to raise an eyebrow to it. That's a ton of energy!
Our first thought was we divided something wrong and it should be 432kg and that is more feasible in my mind. 432kg of wood is a lot of wood by itself. But the answer says 432,000kg of wood and that is a TON.

I mean, that is like asking how much rum Beags consumes in a given time. The answers may be similar...:alien:
 

HBirdman80

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Your math and calculations are correct.

What's throwing you off is the teacher has the wrong number for the energy density of wood. Most energy densities are calculated as MJ/kg, not kJ/kg.

0.02 kJ/kg is about 5 calories. In other words, the teacher's number claims that burning 1 kg of wood would raise the temperature of 5 mLs of water by 1*C total. That's obviously wrong.

The teacher probably converted MJ to kJ by dividing by 1000 instead of multiplying by 1000. Wood is usually considered to be between 15 and 20 MJ/kg, or 15,000 to 20,000 kJ/kg. Using the more conservative of those numbers you'd get 0.576 kg of wood.

I say you call out the teacher and hope for some extra credit :p
 

MWard

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Dude aren't you an attorney? Where did that come from? Hahaha
 

rtparty

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Your math and calculations are correct.

What's throwing you off is the teacher has the wrong number for the energy density of wood. Most energy densities are calculated as MJ/kg, not kJ/kg.

0.02 kJ/kg is about 5 calories. In other words, the teacher's number claims that burning 1 kg of wood would raise the temperature of 5 mLs of water by 1*C total. That's obviously wrong.

The teacher probably converted MJ to kJ by dividing by 1000 instead of multiplying by 1000. Wood is usually considered to be between 15 and 20 MJ/kg, or 15,000 to 20,000 kJ/kg. Using the more conservative of those numbers you'd get 0.576 kg of wood.

I say you call out the teacher and hope for some extra credit :p

That is another part that confused us because when I googled the energy density of wood, it came up with your numbers. Which is a much more reasonable answer.

My wife is going to ask tomorrow but she thinks he did this on purpose so you can't just Google the answers. Some of her teachers have made "mistakes" like this on purpose just to make sure students understand the formulas to use.

Thanks for the help! Maybe the teacher did make an actual mistake and she gets that extra credit!
 

HBirdman80

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Dude aren't you an attorney? Where did that come from? Hahaha
Well, it now turns out that next time my mom gives me grief that "we paid for all that schooling so you could get a degree in biological chemistry and you wasted it by becoming an attorney" I can respond "nu-uh, I can answer random homework questions on an internet golf forum!"

(In reality I do a lot of work in the biotech/pharma/life sciences fields and look at thermodynamic equations on a regular basis.)
 

staticline

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Its probably correct. The math looks right. Wood is a very inefficient method of heat.
 

Ag2979

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I should have never opened this thread. I am starting my day feeling un educated.


Sent from my iPhone using Tapatalk
 

mpeterson

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It's a crazy number because, as HBirdman said, that number for wood is miniscule compared with the real number (I think it's something in the 10+ MJ range, not < 1 kJ/L) . Also, if you want to call out the teacher on something, energy density is J/volume, not J/mass. That's specific energy.
 

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