A liquid has an initial density of 7.00 x 103 kg/m3 at 10°C. If the coefficient of cubic expansivity is 2.1 x 10⁻⁴ /°C, calculate its density at 50°C.

To find the density of the liquid at a new temperature, we use the formula for thermal expansion of density:

$$\rho = \frac{\rho_0}{1 + \gamma \Delta T}$$

where:

• $\rho$ is the final density
• $\rho_0$ is the initial density
• $\gamma$ is the coefficient of cubic expansivity
• $\Delta T$ is the change in temperature

Step 1: Identify the given values.
Initial density, $\rho_0 = 7.00 \times 10^3 \text{ kgm}^{-3}$
Initial temperature, $T_0 = 10^\circ\text{C}$
Final temperature, $T = 10