If two identical mercury drops are combined to form a single drop, then its temperature will

Options

A. decrease
B. increases
C. remains the same
D. None of these

Explanation

To solve the question, "If two identical mercury drops are combined to form a single drop, then its temperature will:", we can follow these steps:

### Step 1: Understand the concept of surface energy
When two identical drops of mercury combine, the total surface area of the resulting single drop is less than the combined surface area of the two smaller drops. Surface energy is related to the surface area of a liquid drop.

**Hint:** Remember that surface energy is proportional to the surface area of the liquid.

### Step 2: Calculate the surface energy before and after combining
Let’s denote the radius of each small drop as \( r \). The surface area of one drop is given by the formula:
\[ A = 4\pi r^2 \]
For two drops, the total surface area would be:
\[ A_{\text{total}} = 2 \times 4\pi r^2 = 8\pi r^2 \]
When these two drops combine, the radius of the new single drop \( R \) can be found using the volume conservation principle. The volume of one drop is:
\[ V = \frac{4}{3}\pi r^3 \]
So, the volume of two drops is:
\[ V_{\text{total}} = 2 \times \frac{4}{3}\pi r^3 = \frac{8}{3}\pi r^3 \]
Setting this equal to the volume of the new drop:
\[ \frac{8}{3}\pi r^3 = \frac{4}{3}\pi R^3 \]
This simplifies to:
\[ R^3 = 2r^3 \implies R = r \sqrt[3]{2} \]

### Step 3: Calculate the surface area of the new drop
Now, the surface area of the new drop with radius \( R \) is:
\[ A_{\text{new}} = 4\pi R^2 = 4\pi (r \sqrt[3]{2})^2 = 4\pi r^2 \cdot 2^{2/3} \]

### Step 4: Compare the surface energies
The surface energy of the two drops before combining is:
\[ E_{\text{initial}} = \sigma \times 8\pi r^2 \]
The surface energy of the new drop is:
\[ E_{\text{final}} = \sigma \times 4\pi R^2 = \sigma \times 4\pi \cdot 2^{2/3} r^2 \]
Since \( 2^{2/3} < 4 \), we can see that:
\[ E_{\text{final}} < E_{\text{initial}} \]
This means that the surface energy has decreased when the drops combine.

### Step 5: Relate surface energy change to temperature change
When the surface energy decreases, the excess energy is converted into thermal energy, which results in an increase in temperature. Therefore, the temperature of the combined drop will increase.

### Conclusion
Thus, when two identical mercury drops are combined to form a single drop, the temperature will increase.

**Final Answer:** The temperature will increase.

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