Equal masses of two substance of density $d_{1} a n d d_{2}$ are mixed together. What would be the density of the mixture.

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Solution

Give that,

Density of first substance = $d_{1}$

Density of second substance = $d_{2}$

Mass of first substance = $m$

Mass of second substance = $m$

Now, the volume of first substance

$V_{1} = \frac{m}{d_{1}}$

The volume of second substance

$V_{2} = \frac{m}{d_{2}}$

Total volume is

$V_{t o t a l} = V_{1} + V_{2}$

$V_{t o t a l} = \frac{m}{d_{1}} + \frac{m}{d_{2}}$

$V_{t o t a l} = \frac{m (d_{1} + d_{2})}{d_{1} d_{2}}$

Total mass is

$M = m + m$

$M = 2 m$

Density of the mixture = total mass/total volume

Density of mixture =

$= \frac{2 m (d_{1} d_{2})}{m (d_{1} + d_{2})}$

$= \frac{2 (d_{1} d_{2})}{(d_{1} + d_{2})}$

Hence, the density of the mixture is $\frac{2 (d_{1} d_{2})}{(d_{1} + d_{2})}$

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Equal masses of two substance of density d1and d2 are mixed together. What would be the density of the mixture.

Equal masses of two substance of density $d_{1} a n d d_{2}$ are mixed together. What would be the density of the mixture.