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Question

An iron scale is calibrated at 0C. The length of a zinc rod is measured to be 100 cm by the scale when the rod and the scale both are at 00C. What will be the length of the rod as measured by the scale when both are at 100C. Given : αiron=1.2×105 C1 and αzinc=2.6×104 C1.

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Solution

Initially both scale and rod will be at zero so iron scale will give correct radially at 100C both will expand.
Let the length of iron and zinc rod at 0oc
length of zinc rod at temperature (t)100oC when measured by sacle that its self undergoes thermal expansion is given as
=Lzt=Lz0[1+(azαI)t]
=100[1+(2.6×1051.2×105)100]
=100[1+[1+(1.4×103)]
=100[1+0.0014]
=100[1.0014]
=100.14cm

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