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Q.

A weight thermometer contains 20 gm of mercury at 0°C and when its temperature is raised to 100°C. 315 gm of mercury is expelled. If the coefficient of linear expansion of glass is 0.0000066 per °C, the coefficient of absolute expansion of mercury is

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a

0.0001600/°C

b

0.0001650/°C

c

0.0001700/°C

d

0.0001798/°C

answer is D.

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Detailed Solution

$γ_{a} = \frac{m_{0} - m_{t}}{m_{t} (T - 0)} \begin{array}{l} = \frac{0 \cdot 315}{(20 - 0 \cdot 315) \times (100 - 0)} \\ = 0 \cdot 00016 /^{\circ} C \end{array}$
Now,
$\begin{array}{l} γ = γ_{a} + γ_{g} = γ_{a} + 3 α \\ = 0 \cdot 00016 + 3 \times (0 \cdot 0000066) \\ = 0 \cdot 0001798 /^{\circ} C \end{array}$
$∴$ Coefficient of real expansion of mercury =0.0001798/°C.

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