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Fahrenheit Scale

A barometer w...

Question

A barometer with a brass scale correct at $0^{o} C$ reads $70 c m$ of mercury on a day when the air temperature is $40^{o} C$ . the correct reading at $0^{o} C$ is (Coefficient of real expansion of mercury, is $0.00018 /^{o} C$ and the coefficient of linear expansion of brass is $0.000018 /^{o} C$ .

60.5 c m

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69.5 c m

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20.5 c m

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50.00 c m

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Solution

The correct option is B $69.5 c m$
If the correct of barometer at $0^{o} C$ is $70 c m$ Then the at $40^{o} C$ the readnig will show
$L = 70 (1 + α_{1} A T)$ $[α_{1} o f b r a s s, △ T = 40 k]$
Similarly mercury expands to $70 c m$ from initial length $L_{o}$
$\Rightarrow L = l_{o} (1 + α_{2} A T)$ $(α_{2} : f o r m e r c u r y)$
It given
$l_{o} = \frac{70 (1 + α_{2} A T}{(1 + α_{2} A T)} = \frac{70 (1 + 1.8 \times 10^{- 5} \times 40}{(1 + 1.8 \times 10^{- 4} \times 40)}$
$l_{o} = 69.55 c m$

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