Question

Density of substance at $0^{\circ }$C is 10 g/cc and at ${100}^{\circ }$C, its density is 9.7 g/cc. the coefficient of linear expansion of the substance is

• A. 1.03 × 10^–4
• B. 3 × 10^–4
• C. 19.7 × 10^–3
• D. 10^–3

Answer 1

The correct option is A 1.03 × 10^–4

Here,
${\rho }_0$ = 10 g/cc
${\rho }_{100}$ = 9.7g/cc, $\alpha$ = ?
From
${\rho }_0$= ${\rho }_{100}$(1 + $\gamma \times 100$)
$\gamma$ = $\frac{{\rho }_0-{\rho }_{100}}{{\rho }_0\times {\rho }_{100}}$ = $\frac{10-9.7}{9.7\times 100}$ = 3.09 $\times {10}^{-4}$
$\alpha$ = $\frac{\gamma }{3}$ = $\frac{3.09\times {10}^{-4}}{3}$ = 1.03 $\times {10}^{-4}{}^{\circ }{C}^{-1}$