NEET-XII-Physics
23: Heat and Temperature
- #12A railway track (made of iron) is laid in winter when the average temperature is 18°C. The track consists of sections of 12.0 m placed one after the other. How much gap should be left between two such sections, so that there is no compression during summer when the maximum temperature rises to 48°C? Coefficient of linear expansion of iron = 11 × 10-6 °C-1.Ans : Given:
Length of the iron sections when there's no effect of temperature on them, Lo = 12.0 m
Temperature at which the iron track is laid in winter, tw = 18 oC
Maximum temperature during summers, ts = 48 oC
Coefficient of linear expansion of iron, `` \alpha `` = 11 × 10-6 °C-1
Let the new lengths attained by each section due to expansion of iron in winter and summer be Lw and Ls, respectively, which can be calculated as follows:
`` {L}_{w}={L}_{0}\left(1+\alpha {t}_{w}\right)``
`` \Rightarrow {L}_{w}=12\left(1+11\times {10}^{-6}\times 18\right)``
`` \Rightarrow {L}_{w}=12.00237\,\mathrm{\,m\,}``
`` {L}_{s}={L}_{0}\left(1+\alpha {t}_{s}\right)``
`` \Rightarrow {L}_{s}=12\left(1+11\times {10}^{-6}\times 48\right)``
`` \Rightarrow {L}_{s}=12.006336\,\mathrm{\,m\,}``
`` \therefore ∆L={L}_{s}-{L}_{w}``
`` \Rightarrow \Delta L=12.006336-12.002376``
`` \Rightarrow \Delta L=0.00396\,\mathrm{\,m\,}``
`` \Rightarrow \Delta L\approx 0.4\,\mathrm{\,cm\,}``
Therefore, the gap (`` \Delta ``L) that should be left between two iron sections, so that there is no compression during summer, is 0.4 cm.
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