If 5 small spherical droplet coalesce to form a bigger drop then temperature of bigger drop in comparison to smaller drops will

Options

A. Decrease
B. Remain same
C. May increase or decrease
D. Increase

Answer

To solve the problem of how the temperature of a bigger drop compares to that of smaller drops when five small spherical droplets coalesce, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Volume Conservation**:
- When five small droplets coalesce to form a larger droplet, the total volume before and after the coalescence remains the same.
- Let the radius of each smaller droplet be \( R_0 \). The volume \( V_0 \) of one small droplet is given by:
\[ V_0 = \frac{4}{3} \pi R_0^3 \]
- Therefore, the total volume of five small droplets is:
\[ V_{\text{total}} = 5 \times V_0 = 5 \times \frac{4}{3} \pi R_0^3 = \frac{20}{3} \pi R_0^3 \]

2. **Volume of the Bigger Drop**:
- Let the radius of the bigger droplet be \( R \). The volume \( V \) of the bigger droplet is:
\[ V = \frac{4}{3} \pi R^3 \]
- Setting the total volume equal to the volume of the bigger droplet, we have:
\[ \frac{20}{3} \pi R_0^3 = \frac{4}{3} \pi R^3 \]
- Canceling \( \frac{4}{3} \pi \) from both sides gives:
\[ 5 R_0^3 = R^3 \]

3. **Finding the Radius of the Bigger Drop**:
- Taking the cube root of both sides, we find:
\[ R = (5)^{1/3} R_0 \]

4. **Relating Volume and Temperature**:
- According to the ideal gas law, for a given amount of gas at constant pressure, the volume \( V \) is directly proportional to the temperature \( T \):
\[ V \propto T \]
- Since the volume of the bigger droplet is greater than that of the smaller droplets (as \( R > R_0 \)), we can conclude that:
\[ V_{\text{bigger}} > V_{\text{smaller}} \implies T_{\text{bigger}} > T_{\text{smaller}} \]

5. **Conclusion**:
- Therefore, the temperature of the bigger drop \( T \) will be greater than the temperature of the smaller drops \( T_0 \):
\[ T > T_0 \]

### Final Answer:
The temperature of the bigger drop in comparison to the smaller drops will be higher.