Creating a Nichrome Heating Coil for 12V, 36W @373K

[pat666]

Homework Statement

A heating coil is to be made, from nichrome wire, which will operate on a 12 V supply and will have a power of 36 W when immersed in water at 373 K. The wire available has a cross-sectional area of 0.10 mm². What length of wire will be required?
(Resistivity of nichrome at 273 K = 1.08 x 10-6 Ωm.
Temperature co-efficient of resistivity of nichrome = 8.0 x 10-5 K-1.)
I think that "Resistivity of nichrome at 273 K = 1.08 x 10-6 Ωm." is meant to say 373K, I will ask tomorrow.

Homework Equations

ρ=ρ⁰ [1+α(T-T₀ ) ]

The Attempt at a Solution

Im thinking that ρ(resistivity) can be changed with P/I^2 then I^2 with V^2/R^2 so i would end up with P*R^2/v^2=ρ⁰ [1+α(T-T₀ ) ] or something like that, I really need some pointers on where to go.

 

[Onamor]

I think that "Resistivity of nichrome at 273 K = 1.08 x 10-6 Ωm." is meant to say 373K

Are you sure the question is not asking you for the length of wire needed in a heating coil, if it is to heat water from 273K (just freezing) to 373K (boiling)? You need a start and an end temp. If you just want to heat water with nichrome then any amount will do...

Think of some more relevant equations. You need a length in there somewhere to solve for it.

 

[pat666]

Yeah it could be that - the question is not written well at all I will ask tomorrow and find out.

 

[pat666]

turns out the question is right.

 

[rock.freak667]

Homework Equations

ρ=ρ₀ [1+α(T-T₀ ) ].

This equation will give you the resistivity at a temperature T. So using the information given and the terms in the equation, what is the resistivity at T=373 K ?

 

[pat666]

p=1.08 x 10-6[1+8.0 x 10-5(373-273)]
will that work??

 

[rock.freak667]

p=1.08 x 10-6[1+8.0 x 10-5(373-273)]
will that work??

Yes that will give you ρ. Now how does ρ relate to the length of wire, resistance and cross-sectional area?

 

[pat666]

hey rock.freak667, sorry for the late reply I was at uni for 10hrs today. I've found resistivity at 373K to be 1.089*10^-6.
then R=p(L/A)
V=IR P=IV so P=V/R*V P=V^2/R R=v^2/P I am not sure if this is right I am just subbing formulas to try and find something useful
I get
V^2/P=p(L/A)
144/36=1.089*10^-6.(L/1.1*10^-7)
L=0.404m

Please reply, I have no idea if this is even close to right
ps-thanks for your help thus far.

 

[rock.freak667]

Ive found resistivity at 373K to be 1.089*10^-6.
then R=p(L/A)

Should be correct assuming you calculated correctly (I didn't check the number)

V=IR P=IV so P=V/R*V P=V^2/R R=v^2/P I am not sure if this is right I am just subbing formulas to try and find something useful
I get
V^2/P=p(L/A)
144/36=1.089*10^-6.(L/1.1*10^-7)
L=0.404m

This should be correct.

 

[pat666]

ok thankyou, as long as the procedure is right.

 

[louza8]

hey man the resistivity of nichrome at 273K is given in the question to be 1.08*10^-6ohmm, using the value 1.089*10^-6ohmm gives you a length required that is 4cm greater. don't know if i would trust the lecturer to mark it correctly, even though its correct with your value.

 

[pat666]

what do you mean? it all checks out - are you talking sig figures or something?>

 

[louza8]

whoops i read it wrong! I'm still getting 0.36m so i'll update this post when i find the difference

edit: okay silly error my bad.