Question

The coefficient of volume expansion of liquid is $\gamma$. The fractional change in its density for $△T$ rise in temperature is ?

• A. $\gamma △T$
• B. $\frac{△T}{\gamma }$
• C. $1+\gamma △T$
• D. $1-\gamma △T$

Answer 1

Answer: (A)

$\gamma △T$

On thermal expansion,

Volumetric expansion is given by

$V=V_0(1+\gamma \Delta T)$. . . . . . . .(1)

We know that, density, $d=\frac{mass}{volume}$

$d=\frac{m}{V}$

where, $m=$ constant

$d\propto \frac{1}{V}$

Density of the liquid varies as

$d=d_0(1+\gamma \Delta T)$

$d=d_0+d_0\gamma \Delta T$

Fractional change in density is

$\frac{d-d_0}{d_0}=\gamma \Delta T$

$\frac{\Delta d}{d_0}=\gamma \Delta T$

The correct option is A.