Question

The coefficient of apparent expansion of mercury in a glass vessel is $153\times 10^{- 6} \, ^\circ \text{C}^{- 1}$ and in a steel vessel is $144\times 10^{- 6} \, ^\circ \text{C}^{- 1}$ , If linear expansion coefficient ( $\alpha $ ) for steel is $12\times 10^{- 6} \, ^\circ \text{C}^{- 1}$ , then that of glass is

• A. $9\times 10^{- 6} \, ^\circ \text{C}^{- 1}$
• B. $6\times 10^{- 6} \, ^\circ \text{C}^{- 1}$
• C. $36\times 10^{- 6} \, ^\circ \text{C}^{- 1}$
• D. $27\times 10^{- 6} \, ^\circ \text{C}^{- 1}$

Answer 1

Answer: (A)

$\gamma _{\text{real}} = \gamma _{\text{app}} + \gamma _{\text{vessel}}$
$\Rightarrow 1 5 3 \times 1 0^{- 6} + \left(\left(\gamma \right)_{\text{vessel}}\right)_{\text{glass}} = 1 4 4 \times 1 0^{- 6} + \left(\left(\gamma \right)_{\text{vessel}}\right)_{\text{steel}}$
Further $\left(\left(\gamma \right)_{\text{vessel}}\right)_{\text{steel}} = 3 \alpha = 3 \times \left(1 2 \times 1 0^{- 6}\right)$
$=36\times 10^{- 6}^{^\circ }\text{C}^{- 1}$
$\therefore 1 5 3 \times 1 0^{- 6} + \left(\left(\gamma \right)_{\text{vessel}}\right)_{\text{glass}} = 1 4 4 \times 1 0^{- 6} + 3 6 \times 1 0^{- 6}$
$\therefore \left(\left(\gamma \right)_{\text{vessel}}\right)_{\text{glass}}=27\times 10^{- 6}^{^\circ }\left(\text{C}\right)^{- 1}$
or $\alpha =\frac{\gamma _{\text{glass}}}{3}=9\times 10^{- 6}^{^\circ }\text{C}^{- 1}$