At which of the following temperatures, the value of surface tension of water is minimum

The correct option is 75°C.

Understanding Surface Tension:
Surface tension is a property of liquid surfaces that causes them to behave like a stretched elastic membrane. It arises due to the cohesive intermolecular forces of attraction acting between the liquid molecules. The molecules at the surface of a liquid experience a net inward pull because there are no liquid molecules above them to balance the cohesive forces from the molecules below and beside them.

Effect of Temperature on Surface Tension:
When the temperature of a liquid increases, the average kinetic energy of its molecules increases. This increased thermal motion makes it easier for the molecules to overcome the intermolecular cohesive forces holding them together. As these cohesive forces weaken, the surface tension of the liquid decreases.

Generally, the relationship between surface tension and temperature is inverse:
$\text{Surface Tension}\propto \frac{1}{\text{Temperature}}$
Therefore, as temperature increases, the surface tension of water decreases.

Analysis of the Given Options:
We are given the following temperatures to compare:
1. 4°C
2. 25°C
3. 50°C
4. 75°C

Since 75°C is the highest temperature among the given options, the intermolecular cohesive forces of water will be at their weakest at this temperature, resulting in the minimum value of surface tension.