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10-1.Thermometry, Thermal Expansion and Calorimetry
medium
A vertical column $50$ $cm$ long at $50°C$ balances another column of same liquid $60 \,cm$ long at $100°C$. The coefficient of absolute expansion of the liquid is
A
$0.005°C^{-1}$
B
$0.0005°C^{-1}$
C
$0.002°C^{-1}$
D
$0.0002°C^{-1}$
Solution
(a) $\frac{{{h_1}}}{{{h_2}}} = \frac{{{\rho _1}}}{{{\rho _2}}} = \frac{{(1 + \gamma \,{\theta _1})}}{{(1 + \gamma \,{\theta _2})}}$ $\left[ {\because \,\rho = \frac{{{\rho _0}}}{{(1 + \gamma \theta )}}} \right]$
$\Rightarrow$ $\frac{{50}}{{60}} = \frac{{1 + \gamma \times 50}}{{1 + \gamma \times 100}}$ $\Rightarrow$ $\gamma = 0.005/^\circ C$
Standard 11
Physics
