1. Tardigrade
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  3. Physics
  4. The reading of a barometer on a steel scale is 75 cm, while the room temperature is 30?C. The linear and volumetric expensions for steel and mercury are 1.2× 10-5oC-1 and 1.8× 10-4oC-1 (γ ), respectively. The atmospheric pressure can be obtained as

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Q. The reading of a barometer on a steel scale is 75 cm, while the room temperature is 30?C. The linear and volumetric expensions for steel and mercury are $ 1.2\times {{10}^{-5}}^{o}{{C}^{-1}} $ and $ 1.8\times {{10}^{-4}}^{o}{{C}^{-1}} $ $ (\gamma ), $ respectively. The atmospheric pressure can be obtained as

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Solution:

From the formula for the linear expansion, the length at 30°C is given as $ {{l}_{\theta }}=75[1+\alpha (30)] $ ...(i) At this temperature suppose the length of mercury column is $ {{l}_{0}} $ while its length at 0°C is $ {{l}_{0}}, $ then $ {{l}_{\theta }}={{l}_{0}}\left[ 1+\frac{1}{3}\gamma (30) \right] $ ...(ii) From Eqs. (i) and (ii), we get $ {{l}_{0}}\left[ 1+\frac{1}{3}\gamma (30) \right]=75[1+\alpha (30)] $ $ \Rightarrow $ $ {{l}_{0}}=7489cm $