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  • When a liquid in a glass vessel is heated its apparent expansion is <img alt="10.30\times 10^{-4}/^{\circ}C" src="http://entrancecorner.oncodecogs.com/gif.latex?10.30%5Ctimes%2010%5E%7B-4%7D/%5E%7B

When a liquid in a glass vessel is heated its apparent expansion is 10.30\times 10^{-4}/^{\circ}C. Same liquid when heated in a metal vessel its apparent expansion is 10.06\times 10^{-4}/^{\circ}C. The coefficient of linear expansion of the metal is (\alpha_{glass}=9\times 10^{-6}/^{\circ}C)

Option: 1

51\times 10^{-6}/^{\circ}C

 

 

 


Option: 2

43\times 10^{-6}/^{\circ}C


Option: 3

25\times 10^{-6}/^{\circ}C


Option: 4

17\times 10^{-6}/^{\circ}C


Answers (1)

best_answer

\gamma_{\mathrm{r}}=\gamma_{\mathrm{1} }+\gamma_{\mathrm{glass}}=\gamma_{2 }+\gamma_{\text {metal }} \ldots \ldots(1)

where \gamma_{1} is the apparent expansion coefficients when the liquid is kept in the glass container and \gamma_{2} is the apparent expansion coefficients when liquid is kept in the metal container
Given,

\begin{aligned} &\gamma_{1}=10.30 \times 10^{-4} \\ &\gamma_{2}=10.06 \times 10^{-4} \\ &\alpha_{\text {glass }}=9 \times 10^{-6} \\ &\gamma_{\text {glass }}=3 \alpha_{\text {glass }}=27 \times 10^{-6} \\ &\gamma_{\text {metal }}=3 \alpha_{\text {metal }} \end{aligned}

Substituting the values in (1)

10.30 \times 10^{-4}+27 \times 10^{-6}=10.06 \times 10^{-4}+3 \alpha_{\text {metal }}

\begin{aligned} &\Rightarrow 24 \times 10^{-6}+27 \times 10^{-6}=3 \alpha_{\text {metal }} \\ &\Rightarrow \alpha_{\text {metal }}=\left(\frac{51}{3}\right) 10^{-6}=17 \times 10^{-6} \end{aligned}

Posted by

SANGALDEEP SINGH

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