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Area and Volume Expansion

A weight ther...

Question

A weight thermometer contains 51 gm of mercury at $0^{\circ} C$ . When placed in an oil bath 1.0 gm is found to overflow. Find the temperature of oil bath. Coefficient of cubical expansion of mercury and glass are ${0.00018}^{\circ} C$ and ${0.000026}^{\circ} C$ respectively.

{1290.87}^{\circ} C

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{129.87}^{\circ} C

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{199.87}^{\circ} C

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{19.87}^{\circ} C

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Solution

The correct option is B ${129.87}^{\circ} C$
$γ_{a} = \frac{m_{0} - m_{t}}{m_{t} . t} o r t = \frac{m_{0} - m_{t}}{m_{t} . γ_{a}} G i v e n t h a t m_{0} = 51 g m, m_{t} = m_{0} - o v e r f l o w i n g m a s s = 51 - 1 = 50 g m γ_{a} = 0.00018 /^{\circ} C γ_{g} = 0.00026 /^{\circ} C ∴ γ_{a} = γ_{r} - γ_{g} = 0.00018 - 0.000026 = 0.000154 /^{\circ} C ∴ t = \frac{51 - 50}{50 \times 0.000154} = \frac{1}{0.0077} = {129.87}^{\circ} C ∴ T e m p e r a t u r e o f b a t h = {129.87}^{\circ} C$

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