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An aluminum measuring rod, which is correct at 5.0 C measures a certain distance as 88.42...

An aluminum measuring rod, which is correct at 5.0 C measures a certain distance as 88.42 cm at 35.0 C.Determine the error in measuring the distance due to the expansion of the rod. If this aluminum rod measures a length of steel as 88.42cm at 35.0 C, what is the correct length of the steel at 35 degrees C? The coefficient of linear expansion of aluminum is 22 x10^-6 C^-1.

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Answer #1

Initial temp t = 5 oC

Final temp t ‘ = 35 oC

Initial length L = 88.42 cm

Coefficient of linear expansion  α = 22 x 10 -6 /oC

We know   α = ( L ‘ –L )/ [ L ( t’-t ) ]

From this The error in measuring the distance due to the expansion of the rod

      L ‘ – L = αL ( t’-t )

                 = 0.05835 cm

Answer to (a) 0.058 cm

And Correct length of copper = 88.44 cm - 0.058 cm = 88 cm
Answer to (b) 88 cm

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