# I am pretty sure my answer is right!!

#### Integrator741

Jun 16, 2013
125
Good evening,

I am practising my ability to manipulate units and stuff, and I came across this question that doesn't sound that hard but I just can't get the right answer.

"The electricity meter on a plant initially reads 6032 kWh. If the plant now runs for 73 minutes at a steady power consumption of 320 kW determine a) Energy consumed in MJ b) The final reading of the meter"

Answers:. a) 1401.6 MJ; b) 6421.3 kWh

My working out is:

320 kWh/60min = 5.3 kW per min.
5.3 kW per min * 73 min = 386.9 kWh
so the final reading will be 6032 + 386.9 = 6419 kWh

now to convert 386.9 to MJ:

1kWh = 3.6 MJ

386.9/3.6 = 107.472 MJ;

I am close with a) but b)... no idea.

Thanks

#### davenn

Moderator
Sep 5, 2009
14,273
now to convert 386.9 to MJ:

1kWh = 3.6 MJ

386.9/3.6 = 107.472 MJ;

I am close with a) but b)... no idea.

why did you divide by 3.6 ? it should be multiply

1kWh = 3.6 ...... ( 3.6MJ for each kWh)
2kWh = 7.2
10kWh = 36

etc

386.9 x 3.6 = ..... ?

you now work that out

cheers
Dave

#### dorke

Jun 20, 2015
2,342
Very simple:
Do not round the results!

a) 320*(73/60)*3.6= ??
b) 320*(73/60)+6032 = ??

Last edited by a moderator:

Moderator
Sep 5, 2009
14,273
Dorke

#### Integrator741

Jun 16, 2013
125
Very simple:
Do not round the results!

a) 320*(73/60)*3.6=1401.6
b) 320*(73/60)+6032 =6421.3
Thanks, I didn't think that it would make such a significant difference. Again thanks. Maybe you'd be able to help me with another question, about some copper wire coiled around a tube.

"Copper wire (density 8900) of cross-section 1.7mm^2 is coiled onto a long cylindrical former. The resulting coil has 820 turns, and diameter 0.13m. Find the mass of wire in KG."

What I did:

First I need to know the length of the catble - length of one turn is (pi)*Diameter of the cylinder. (pi)*0.13m = 0.408m;
Total length of the cable is: 0.408m * 820 turns = 334.9m;

then I need to calculate the volume of the cable in order to calculate its mass.

To find volume of the cylinder - I need diameter.

I know that area=(pi)*r^2 so 0.13=(pi)*r^2; (solve for r)
r=(square root)0.13/(pi) = 0.2m - so diameter is 0.4m;

Volume of the cylinder is: ((pi)*d^2*l)/4 = I got 42.08m^3, then to find mass I multiply my answer by the given density and I get: 374512kg and the actual answer is 5.0669 kg - what the hell?

#### davenn

Moderator
Sep 5, 2009
14,273
I like Dorke's way, at least it gives the expected answer

his gives 389.333, where as yours gives 386.9 and of course that made the answer
wrong for you and me as I used your number

#### dorke

Jun 20, 2015
2,342
Thanks, I didn't think that it would make such a significant difference. Again thanks. Maybe you'd be able to help me with another question, about some copper wire coiled around a tube.

"Copper wire (density 8900) of cross-section 1.7mm^2 is coiled onto a long cylindrical former. The resulting coil has 820 turns, and diameter 0.13m. Find the mass of wire in KG."

What I did:

First I need to know the length of the catble - length of one turn is (pi)*Diameter of the cylinder. (pi)*0.13m = 0.408m;
Total length of the cable is: 0.408m * 820 turns = 334.9m;

then I need to calculate the volume of the cable in order to calculate its mass.

To find volume of the cylinder - I need diameter.

I know that area=(pi)*r^2 so 0.13=(pi)*r^2; (solve for r)
r=(square root)0.13/(pi) = 0.2m - so diameter is 0.4m;

Volume of the cylinder is: ((pi)*d^2*l)/4 = I got 42.08m^3, then to find mass I multiply my answer by the given density and I get: 374512kg and the actual answer is 5.0669 kg - what the hell?

I think they are talking about a coil raped around a cylinder.
That means the cylinder is hollow:
there is only copper wire on it's "outer- case" .

So you have a copper wire with a cross-section of
1.7mm^2 wrapped around the cylinder of diameter 0.13m

1.You did o.k with calculating the wire length,
to be more accurate you need to add the diameter of the wire to the diameter of the cylinder!)-again don't round numbers.
2.You need to convert the cross-section to meters and multiply by the length to find the wires volume in meters^3
3.Last multiply by the density (in meters^3) to get the result.

#### Integrator741

Jun 16, 2013
125
I think they are talking about a coil raped around a cylinder.
That means the cylinder is hollow:
there is only copper wire on it's "outer- case" .

So you have a copper wire with a cross-section of
1.7mm^2 wrapped around the cylinder of diameter 0.13m

1.You did o.k with calculating the wire length,
to be more accurate you need to add the diameter of the wire to the diameter of the cylinder!)-again don't round numbers.
2.You need to convert the cross-section to meters and multiply by the length to find the wires volume in meters^3
3.Last multiply by the density (in meters^3) to get the result.View attachment 23010
Thank you - I got it now.
One question though, I see that I get my answer in grams, why is that?

#### dorke

Jun 20, 2015
2,342
"I see that I get my answer in grams, why is that?

#### Integrator741

Jun 16, 2013
125
Cable length = turns*circumference = 820 * ((pi)*0.13) = 334.89
Volume = (1.7*10^-3) * 334.89 = 0.56932 m^3

Volume*density = 0.56932 * 8900 = 5066.9

#### davenn

Moderator
Sep 5, 2009
14,273
Volume*density = 0.56932 * 8900 = 5066.9

One question though, I see that I get my answer in grams, why is that?

because the 8900 is 8900 grams / m3 ( 8.9 g / cm3 )
so you ended up with 5066.9 grams = 5.066kg

also again you are still rounding off ... stop it !!

you should be using 8.96 g / cm3

#### dorke

Jun 20, 2015
2,342
Dave,
You both got it wrong...

The density of copper is indeed 8900Kg/m^3 not gr.
A 1x1x1 meter cube of copper weighs about 9tons not 9Kg...

The problem is in transferring the wire diameter from mm^2 to m^2
the factor should be 1x 10^-6 and not 1x10^-3...

#### davenn

Moderator
Sep 5, 2009
14,273
DOH ... that will teach me for doing maths at 6 am !!!

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