Question

When a liquid in a glass vessel is heated, its apparent expansion is 10.30 $\times {10}^{-4}{}^{\circ }{C}^{-1}$ . When the same liquid is heated in a metal vessel, its apparent expansion 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 × 10^–6°C^–1
• B. 17 × 10^–6°C^–1
• C. 25 × 10^–6°C^–1
• D. 43 × 10^–6°C^–1

Answer 1

The correct option is B 17 × 10^–6°C^–1

Here,
${\gamma }_{ag}$ = 10.30 $\times {10}^{-4}{}^{\circ }{C}^{-1}$
${\gamma }_{am}$ = 10.06 $\times {10}^{-4}{}^{\circ }{C}^{-1}$
${\alpha }_a$ = 9 $\times {10}^{-6}{}^{\circ }{C}^{-1}$, ${\alpha }_m$ = ?
Now, ${\gamma }_r$ = ${\gamma }_{ag}$ + ${\gamma }_{glass}$ = ${\gamma }_{am}$ + ${\gamma }_m$
$\therefore$10.30 $\times {10}^{-4}+3\times 9+\times {10}^{-6}=10.06\times {10}^{-4}+g_m$[$\therefore$ = 3 $\times {\alpha }_a$]
$\therefore$ ${\gamma }_m$ = (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 $\times {10}^{-6}{}^{\circ }{C}^{-1}$