Question

When a liquid in a glass vessel is heated, its apparent expansion coefficient is $10.30\times 10^{-4}{}^{\circ }{C}^{-1}$ . When the same liquid is heated in a metal vessel, its apparent expansion coefficient is $10.06\times 10^{-4}{}^{\circ }{C}^{-1}$ . If the coefficient of linear expansion of glass = $9\times 10^{-6}{}^{\circ }{C}^{-1}$ . What is the coefficient of linear expansion of metal?

• A. $51\times 10^{-6}{}^{\circ }{C}^{-1}$
• B. $17\times 10^{-6}{}^{\circ }{C}^{-1}$
• C. $25\times 10^{-6}{}^{\circ }{C}^{-1}$
• D. $43\times 10^{-6}{}^{\circ }{C}^{-1}$

Answer 1

Answer: (B)

Here, ${\gamma }_{ag}=10.30\times 10^{-4}{}^{\circ }{C}^{-1}$
${\gamma }_{am}=10.06\times 10^{-4}{}^{\circ }{C}^{-1}$
${\alpha }_g=9\times 10^{-6}{}^{\circ }{C}^{-1},{\alpha }_m=?$
Now, ${\gamma }_r={\gamma }_{ag}+{\gamma }_g={\gamma }_{am}+{\gamma }_m$
$\therefore 10.30\times 10^{-4}+3\times 9\times 10^{-6}=10.06\times 10^{-4}+{\gamma }_m\left[\because {\gamma }_g=3\times {\alpha }_a\right]$
$\therefore {\gamma }_m=(10.30+0.27-10.06)10^{-4}=0.51\times 10^{-4}$
${\alpha }_m=\frac{1}{3}{\gamma }_m=\frac{0.51\times 10^{-4}}{3}$
$=0.17\times 10^{-4}=17\times 10^{-6}{}^{\circ }{C}^{-1}$