Question

A quantity of mercury occupies 400.0 cm^3 at 0°C. What volume will it occupy when heated to 50°C? Mercury has a volume expansion coefficient of 180 × 10^-6 K-1. A) 450 cm^3B) 409.7 cm^3C) 403.6 cm^3D) 401.8 cm^3

Answer 1

Answer : The correct option is, (C) $403.6cm^3$

Explanation :

The formula used for the volume expansion coefficient is:

$V_{final}=V_{initial}\times (1+\gamma \Delta T)$

where,

$V_{final}$ = final volume of mercury = ?

$V_{initial}$ = initial volume of mercury = $400.0cm^3$

$\gamma$ = volume expansion coefficient = $180\times 10^{-6}K^{-1}$

$\Delta T$ = change in temperature = $50^oC-0^oC=50^oC$

Now put all the given values in the above formula, we get:

$V_{final}=400.0\times [1+(180\times 10^{-6}\times 50)]$

$V_{final}=403.6cm^3$

Therefore, the final volume of mercury is $403.6cm^3$