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=> In the beginning, the rod and the scale both are at 0°C. Iron scale and rod both will expand at 100° C.
Suppose the length of zinc rod at 0 °C, Lz0 = 100 cm
αiron = 1.2 * 10⁻⁵ C⁻¹
αzink = 2.6 * 10⁻⁵ C⁻¹
=> The length of the rod as measured by the scale when both are at 100°C as it undergoes thermal expansion itself, L z t :
= L z 0 { 1 + ( αzinc − α Iron ) t }
= 100 {1 + ( 2.6 × 10 ⁻⁵ − 1.2 × 10 ⁻⁵) 100 }
= 100 {1 + ( 1.4 × 10 ⁻⁵ )10² }
= 100 { 1 + 1.4 * 10⁻³ }
= 100 {1 + 1.4/1000 }
= 100 { 1 + 0.0014}
= 100 { 1.0014 }
= 100.14 c m
Thus, the length of the rod as measured by the scale when both are at 100°C will be 100.14 cm.
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