Question

The density of a liquid at ${100}^0$C is $8.0$ gm$/c{m}^3$ and at $0^0$C is $8.4$ gm$/c{m}^3$, the coefficient of cubical expansion of the liquid is?

• A. ${10}^{-4}{/}^{0}C$
• B. $5\times {10}^{-4}{/}^{0}C$
• C. $8\times {10}^{-4}{/}^{0}C$
• D. $4\times {10}^{-4}{/}^{0}C$

Answer 1

The correct option is A ${10}^{-4}{/}^{0}C$

Use the formula of volumetric thermal expansion,$V=V₀(1+3\alpha \times \Delta T)$

we know,$density=\frac{mass}{Volume}$

because mass can't be change if temperature change.so,formula of thermal expansion for density,

$d=d₀(1+3\alpha \times \Delta T)$

$9.7=\frac{10}{[1+3\alpha \times (100-0\left)\right]}$

$9.7=\frac{10}{[1+300\alpha ]}$

$9.7+2910\alpha =10$

$2910\alpha =0.3$

$\alpha =0.00010309$

$\alpha =1.0309\times {10}^{-4}$