NEET-XII-Physics
23: Heat and Temperature
- #16A 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-1.Ans : Given:
Temperature at which a metre scale gives an accurate reading, T1 = 20 °C
The value of variation admissible, ΔL = 0.055 mm = 0.055 × 10-3 m, in the length, L0 = 1 m
Coefficient of linear expansion of steel, α = 11 × 10-6 °C-1
Let the range of temperature in which the experiment can be performed be T2.
We know: ΔL = L0 αΔT
`` \Rightarrow 0.055\times {10}^{-3}=1\times 11\times {10}^{-6}\times \left({T}_{1}\pm {T}_{2}\right)``
`` \Rightarrow 5\times {10}^{-3}=\left(20\pm {T}_{2}\right)\times {10}^{-3}``
`` \Rightarrow 20\pm {T}_{2}=5``
`` \Rightarrow \text{E}\,\mathrm{\,ither\,}{T}_{2}=20+5=25°\,\mathrm{\,C\,}``
`` \,\mathrm{\,or\,}{T}_{2}=20-5=15°\,\mathrm{\,C\,}``
Hence, the experiment can be performed in the temperature range of 15 °C to 25 °C .
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