Question

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

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

Answer 1

The correct option is A $\gamma \Delta T$

The equation for the volume expansion is given as:

$\Delta V=V_o\gamma \times \Delta T$

Where the change in volume i.e. $\Delta$ will be equal to the initial volume $V_o$ multiplied by the coefficient of volume expansion, i.e. $\gamma$ and by the temperature change.

Relative change in volume expansion,

$\frac{\Delta V}{V}=\gamma \times \Delta T$

So, new volume after expansion will be,

$=V+V\times \gamma \times \Delta T.$

Thus fractional change in volume $=\frac{\Delta V}{V}=\gamma \times \Delta T$

So, fraction change in density, as mass will be constant, will also be same as above.

Thus option A is correct.