# expanding steel problem

• Jul 10th 2005, 12:44 AM
_jay_
i'm finding this question difficult to work out,any help would be great thanks!
here is the question:

A piece of steel is 11.5 meters long at 22 degrees Celsius. It is heated to 1221 degrees Celsius, close to its melting temperature. How long is it?
• Jul 10th 2005, 03:03 AM
ticbol
It should not be that difficult. It is only a substitution, or plugging in, problem. Nothing to analyze really. That is if you know the formula and constants to use.

The question is about linear thermal expansion of a length of steel.
In Physics we learned for this case that
"the change in length is proportinal to the change in temperature"
delta L ----> L*(delta T)
delta L = k*[L*(delta T)] -------(i)

where
>>>delta L is (change in length) = (final length minus initial length)
Or, (final length) = (initial length) +(delta L)

>>>k = constant of proportionality = average coefficient of linear expansion.
For steel, k = 11*[10^(-6)] per degree Centigrade

>>>L = initial length

>>>delta T = change in temperature = (final temp. minus initial temp.)

Given:
L = 11.5 m
delta T = (1221 -22) = 1099 deg Celsius

So, substituting all those into (i),
delta L = [11*10^(-6)]*[11.5 * 1099] = 0.139 m

Therefore, that piece of steel is
11.5 + 0.139 = 11.639 m long
when its temperature is 1221 degrees Celsius.
• Jul 10th 2005, 09:01 AM
_jay_
thanks that really helped