the length of an iron rod is measured by a brass scale. When both of them are at 20C, the length is 80 cm. The length of the rod at 100C as measured by the scale at 100C is[The coefficient of linear expansion of brass and iron are 24x10^-6(degree C)^-1 and 18x10^-6(degree C)^-1 respectively.]
Answers
Given : the length of an iron rod is measured by a brass scale. When both of them are at 20° C, the length is 80 cm.
To find : The length of the rod at 100° C as measured by the scale at 100° C.
Solution : when temperature increases, length of iron rod and length of brass scale also increase. so length of iron rod with respect to brass scale is the difference between the lengths of iron and brass at 100°C.
i.e., ∆L = L'_brass - L'_iron
= L(1 + α₁∆T) - L(1 + α₂∆T)
= L(α₂ - α₁)∆T
= 80cm × (24 × 10^-6 - 18 × 10^-6) × (100 - 20)
= 80 × 6 × 10^-6 × 80
= 3.84 × 10¯² cm
⇒L' - L_0 = 3.84 × 10¯² cm
⇒L' = 80cm + 0.0384 cm = 80.0384 cm
Therefore the length of rod at 100°C as measured by the brass scale at 100°C is 80.0384 cm .
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