1.5 Density variation with temperature

1.1 Ideal liquid
1.2 Density of a liquid $\left( \rho \right)$
1.3 Relative density of a liquid $(RD)$
1.4 Density of a mixture of two or more liquid
1.5 Density variation with temperature
1.6 Density variation with pressure

2.1 Atmospheric pressure
2.2 Pressure variation with depth
2.3 Measurement of pressure
2.4 Pressure difference in accelerating fluids

5.1 Equation of continuity
5.2 Bernoulli's theorem
5.3 Application of Bernoulli's theorem

7.1 Terminal velocity $\left( {{v_T}} \right)$

8.1 Surface tension
8.2 Variation in surface tension
8.3 Surface energy $(E)$
8.4 Excess pressure

9.1 Capillarity
9.2 Rise of a liquid in a tube of insufficient lengthz

Density is given as, $$\rho = \frac{m}{V}$$

As we know that the mass of the liquid remains constant with the change in temperature.

Variation of volume with temperature is given by, $$V' = V(1 + \gamma \Delta T)$$where,

$V$: Initial volume of the liquid

$V'$: Final volume of the liquid

$\gamma $: Thermal coefficient of volume expansion

$\Delta T$: Change in temperature

So, $$\begin{equation} \begin{aligned} \frac{{\rho '}}{\rho } = \left( {\frac{m}{{V'}}} \right)\left( {\frac{V}{m}} \right) \\ \frac{{\rho '}}{\rho } = \frac{V}{{V\left( {1 + \gamma \Delta T} \right)}} \\ \rho ' = \frac{\rho }{{\left( {1 + \gamma \Delta T} \right)}} \\\end{aligned} \end{equation} $$