Verified Solution • 2025–26 Session moderate

QPages 12-14: Q16: HC Verma: Concepts of Physics - Volume 2 Heat and Temperature Pages 12-14: Q16 Solution: A metre scale made of steel reads accurately at 20�C. In a…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often treat the linear expansion formula $\Delta L = \alpha L_0 \Delta T$ as giving only a positive length change, ignoring that $\Delta T$ can be negative and the scale can contract as well; the required accuracy $0.055\,\text{mm}$ is a two‑sided tolerance, so one must use $|\alpha\Delta T|\le \frac{0.055\times10^{-3}}{1}$ and solve for $\Delta T$ to obtain both upper and lower temperature limits.

A metre scale made of steel reads accurately at 20�C. In a sensitive experiment, distances accurate up to 0.055 mm in 1 m are required. Find the range of temperature in which the experiment can be performed with this metre scale. Coefficient of linear expansion of steel = 11×10−6 �C−111 \times 10^{-6} \text{ �C}^{-1}.

Step-by-Step Verified Solution

**Answer:** Range: 15�C15�\text{C} to 25�C25�\text{C} **Step-by-Step Explanation:** Accuracy required: 0.0550.055 mm in 1 m = 5.5×10−55.5 \times 10^{-5}. ∣αΔT∣≤5.5×10−5|\alpha \Delta T| \le 5.5 \times 10^{-5} 11×10−6×∣ΔT∣≤5.5×10−511 \times 10^{-6} \times |\Delta T| \le 5.5 \times 10^{-5} ∣ΔT∣≤5�C|\Delta T| \le 5�\text{C} Temperature range: 20±5=15�C20 \pm 5 = 15�\text{C} to 25�C25�\text{C}.

All Questions in this Chapter

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