   Chapter 10, Problem 22P

Chapter
Section
Textbook Problem

A construction worker uses a steel tape to measure the length of an aluminum support column. If the measured length is 18.700 m when the temperature is 21.2°C, what is the measured length when the temperature rises to 29.4°C? Note: Don’t neglect the expansion of the tape.

To determine
The measured length.

Explanation

Given Info: The initial length of aluminium tape ( L0 ) is 18.700 m. The temperature changes from T1=21.2οC to T2=29.4οC . The co-efficient of linear expansion ( αAl ) of aluminum is 24×106/οC . The co-efficient of linear expansion ( αs ) of steel is 11×106/οC .

The final length of the aluminum column is equal to the final length of the tape. Therefore,

(L0)new[1+αs(T2T1)]=L0[1+αAl(T2T1)]

• (L0)new is the measured length.

On Re-arranging,

(L0)new=L0[1+αAl(T2T1)1+αs(T2T1)]

Substitute 18

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