When a thermometer is taken from the melting ice to warm liquid , the mercury level rises to `(2^(th))/(5)` of the distance between the lower and the upper fixed points . The temperature of liquid in K is a) 217.15 b) 313.15 c) 220 d) 330

Options

A. `217.15`
B. `313.15`
C. `220`
D. 330

Explanation

To solve the problem, we need to determine the temperature of the liquid in Kelvin based on the information given about the thermometer's reading.

### Step-by-Step Solution:

1. **Understanding the Fixed Points**:
- The thermometer is calibrated between two fixed points: the melting ice (0°C) and the boiling water (100°C). This means that the distance between these two points represents a temperature range of 100°C.

2. **Finding the Fraction of the Distance**:
- The problem states that the mercury level rises to \( \frac{2}{5} \) of the distance between the lower (0°C) and upper (100°C) fixed points.
- Therefore, we can calculate the temperature corresponding to this fraction:
\[ T = \frac{2}{5} \times 100°C \]

3. **Calculating the Temperature in Celsius**:
- Performing the multiplication:
\[ T = \frac{2 \times 100}{5} = \frac{200}{5} = 40°C \]

4. **Converting Celsius to Kelvin**:
- To convert the temperature from Celsius to Kelvin, we use the formula:
\[ T(K) = T(°C) + 273 \]
- Substituting the value we found:
\[ T(K) = 40 + 273 = 313 K \]

5. **Final Answer**:
- The temperature of the liquid in Kelvin is \( 313.15 K \).

### Conclusion:
The correct option is **(b) 313.15**.

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