Which graph represents the variation of surface tension with temperature over small temperature ranges for water?

Options

A.
B.
C.
D.

Answer

To determine which graph represents the variation of surface tension with temperature over small temperature ranges for water, we can follow these steps:

### Step 1: Understand the relationship between surface tension and temperature
Surface tension is a property of liquids that decreases as the temperature increases. This means that as the temperature rises, the surface tension of water will decrease.

### Step 2: Use the equation for surface tension variation
The variation of surface tension (T) with temperature (t) can be expressed with the following linear equation for small temperature differences:
\[ T = T_0 (1 - \alpha t) \]
Where:
- \( T_0 \) is the surface tension at 0 degrees Celsius,
- \( \alpha \) is the temperature coefficient of surface tension,
- \( t \) is the temperature in degrees Celsius.

### Step 3: Analyze the equation
From the equation, we can see that:
- As temperature \( t \) increases, the term \( (1 - \alpha t) \) decreases.
- This indicates that \( T \) (surface tension) decreases linearly with increasing temperature.

### Step 4: Identify the graph type
Since the relationship is linear and has a negative slope (indicating that surface tension decreases with increasing temperature), the graph that represents this relationship will be a straight line that slopes downwards.

### Step 5: Select the correct graph
Among the options provided:
- A negative slope graph represents the linear decrease of surface tension with temperature.
- Therefore, the correct answer is option B, which depicts a linear graph with a negative slope.

### Final Answer
The graph that represents the variation of surface tension with temperature over small temperature ranges for water is option B (a linear graph with a negative slope).

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