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
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)
>>>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.)
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.