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Q.
The variation of density of a solid with temperature is given by the formula
Thermal Properties of Matter
Solution:
From the definition of $\gamma$, we know it is defined as change in volume per volume per unit temperature difference.
So, $\gamma=\frac{ V _{2}- V _{1}}{ V _{1}\left( t _{2}- t _{1}\right)}$
Or $V _{2}= V _{1}\left[1+\gamma\left( t _{2}- t _{1}\right)\right]$
Now, density $=$ mass/ volume, So, replacing $V _{1}$ with $\frac{ M }{ d _{1}}$ and $V _{2}$ with $\frac{ M }{ d _{2}}$ we have,
$d _{2}=\frac{ d _{1}}{\left[1+\gamma\left( t _{2}- t _{1}\right)\right]}$