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The fuel value of peanuts is 25 kj/ gram. If an average adult needs 2800 kilocalories of energy a day, what mass of peanuts would meet an average adult's energy needs for the day? Assume all of the fuel value of the peanuts can be converted to useful energy.

- lilai3

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- UnkleRhaukus

1 adult's energy requirement = 2800 kc/day
how many kilo calories are required "for the day"?

- lilai3

2800?

- UnkleRhaukus

yes,

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## More answers

- UnkleRhaukus

how many joules of energy, is 1 kilocalorie?

- lilai3

4.184

- UnkleRhaukus

so how many joule of energy is 2800 kilocalories,
i.e. 2800 [kc] x 4.184 [j/kc] =

- lilai3

11715.2 joules?

- UnkleRhaukus

So , we have a requirement of 11715.2 [ j ] .
And, we know the fuel value of peanuts is 25 [ kj / g ]

- lilai3

yeah

- UnkleRhaukus

wait a minute
4.184 kilojoules* of energy, is 1 kilocalorie!

- UnkleRhaukus

so we have 11715.2 [kj ] .

- lilai3

yeah.
how do you set it up?

- UnkleRhaukus

food value [ kj/g ] = energy [ kj ] / mass [ g ]
so
mass [ g ] = energy [ kj ] / food value [ kj/g ]

- lilai3

mass = 4.184 kj / 25?

- lilai3

oh and then you just divide it and the answer will be in grams?

- UnkleRhaukus

yeah , what do you get?

- UnkleRhaukus

doe it seem like a reasonable result?

- lilai3

0.17 grams

- lilai3

is that correct?

- UnkleRhaukus

wait, a minute

- UnkleRhaukus

mass of peanuts [g] = 11715.2 [kj ] / 25 [kj/g]

- UnkleRhaukus

the energy required is the 11715.2 [kj]

- lilai3

468.61 grams?

- lilai3

that feels more correct than the answer I got less than 1 last time

- UnkleRhaukus

yeah, about half a kilo seems reasonable to me

- lilai3

so basically we just had to convert kilocalories to kilojoules to get the mass?

- UnkleRhaukus

first, we found the energy required in the time considered (one day)
then we converted the energy from kilocalories to kilojoules
and then from kilojoules, we used the fuel value of peanuts to find the mass of peanuts that provides this energy

- lilai3

Oh, okay. I see how it relates to the problem now. Thanks.

- lilai3

I have one more if you don't mind.

- lilai3

The specific heat of aluminum is 0.902 joule / g x Celsius and that of silver is 0.235 joules / grams x Celsius. You have two spoons of equal masses. One is made of aluminum and other silver. Which spoons would increase in temperature faster in a pot of hot soup? Why?

- lilai3

This one is so hard

- lilai3

Do you think you can help me with this one?

- UnkleRhaukus

if we look at the units of specific heat capacity, that is \([\frac{\textrm j}{\text g\,°\text C}]\)

- lilai3

yep

- UnkleRhaukus

the units say the specific heat capacity is: the energy [joules]
to heat a mass [grams] by a temperature [°C]

- lilai3

yeah, i understand that.

- UnkleRhaukus

so which spoon takes the lesser amount energy transfer to heat up

- lilai3

Would it be the silver? Since 0.235 is less than 0.902 joules? So then it would take less amount for energy to heat?

- UnkleRhaukus

yep,
from experience, we know that metals are good conductors of heat
[ metals feel very cold on a normal day, or burn us quickly if they are hot and we touch them ]

- UnkleRhaukus

silver is a 'better' metal than aluminium
more shiny and much better conductor

- lilai3

so the aluminum will be faster to heat up in a pot of hot soup because 0.902 joules is greater than 0.235 joules.

- UnkleRhaukus

nope the Al takes more energy to transfer temperature

- UnkleRhaukus

(which takes more time)

- lilai3

wait so the higher the joule, the more energy it requires for it to heat something up?

- UnkleRhaukus

more to heat it up AND more to cool it down

- lilai3

so silver will increase the temperature faster due to it's smaller joule, which makes the process of heating faster than the alumiunum?

- UnkleRhaukus

the mass are the same ,
the comparison is the joule to degree ratio

- lilai3

So my answer is going to be
The silver spoon will increase in temperature faster than aluminum since silver has a smaller joule. The higher the number of joules, the more energy it requires to heat up something.

- lilai3

is it okay? should i add anything?

- UnkleRhaukus

The silver spoon will increase in temperature faster than aluminium spoon, since the masses are the same, and silver has a smaller specific heat than aluminium: The greater the specific heat, the more joules of energy must transfer to the spoon; the more time is required for soup to heat the spoon by a given amount.

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