Moderate
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Question
Find the length of an iron rod at 110°C if at 10°C, the length of the rod is 20 cm. [Volume expansion coefficient of iron = 36 × 10⁻⁶ /°C]
WBBSE
Class X
Physical Science
Thermal phenomena
03 Mark
2025
Answer
Initial length (L₁) = 20 cm
Initial temperature = 10°C
Final temperature = 110°C
Rise in temperature (ΔT) = 110 − 10 = 100°C
Volume expansion coefficient (γ) = 36 × 10⁻⁶ /°C
Linear expansion coefficient (α) = \frac{\gamma}{3}
= \frac{36 \times 10^{-6}}{3}
= 12 × 10⁻⁶ /°C
Using the formula, L₂ = L₁ (1 + αΔT)
L₂ = 20 (1 + 12 × 10⁻⁶ × 100)
L₂ = 20 (1 + 0.0012)
L₂ = 20 × 1.0012
L₂ = 20.024 cm
Hence, the length of the iron rod at 110°C is 20.024 cm.
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