A small quantity of a liquid which dows not mix with water sinks to the bottom at `20^@`C, the densities of the liquid and water being 1021 and `990 kg//m^(3)`, respectively. To what teperature must the mixture be uniformly heated in order that the liquid forms globules which just float on water ? the cubical expansion of the liquid and water over the temperature ranges is `85xx10^(-5)//K` and `45xx10^(-5)//K` respectively.

Explanation

To solve the problem step by step, we will use the concept of density changes due to thermal expansion.

### Step 1: Understand the problem
We have a liquid that sinks in water at 20°C. The densities of the liquid and water are given as 1021 kg/m³ and 990 kg/m³, respectively. We need to find the temperature at which the liquid will just float on water.

### Step 2: Write the formula for density change
The density of a substance changes with temperature due to thermal expansion. The new density (d) can be expressed as:
\[ d = \frac{d_0}{1 + \beta \Delta T} \]
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