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QPages 12-14: Q10: HC Verma: Concepts of Physics - Volume 2 Heat and Temperature Pages 12-14: Q10 Solution: A concrete slab has a length of 10 m on a winter night when the …

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often write $Delta L=\alpha\Delta T$ and then add it directly to $L_0$, giving $L=L_0+\alpha\Delta T$. The correct relation is $Delta L=\alpha L_0\Delta T$, so $L=L_0(1+\alpha\Delta T)$. Remember to multiply the temperature term by the original length before adding.

A concrete slab has a length of 10 m on a winter night when the temperature is 0�C. Find the length of the slab on a summer day when the temperature is 35�C. The coefficient of linear expansion of concrete is 1.0×10−5 �C−11.0 \times 10^{-5} \text{ �C}^{-1}.

Step-by-Step Verified Solution

**Answer:** L=10.0035 mL = 10.0035 \text{ m} **Step-by-Step Explanation:** L0=10L_0 = 10 m, ΔT=35�C\Delta T = 35�\text{C}, α=1.0×10−5\alpha = 1.0 \times 10^{-5} /�C.
L=L0(1+αΔT)=10(1+1.0×10−5×35)=10(1.00035)=10.0035 mL = L_0(1 + \alpha \Delta T) = 10(1 + 1.0 \times 10^{-5} \times 35) = 10(1.00035) = 10.0035 \text{ m}

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