when a thermometer is taken from the melting ice to a warm liquid, the mercury level rises to `(2)/(5)th` of the distance between the lower and the upper fixed points. Find the temperature of liquid in ` .^(@)C` and K.

Explanation

To find the temperature of the warm liquid when the thermometer is taken from melting ice, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Fixed Points**:
The lower fixed point (melting ice) is at 0°C and the upper fixed point (boiling water) is at 100°C. The total distance between these two points is 100°C.

2. **Determine the Rise of Mercury**:
The problem states that the mercury level rises to \( \frac{2}{5} \) of the distance between the lower and upper fixed points. Therefore, we calculate the rise of mercury as follows:
\[ \text{Mercury rise} = \frac{2}{5} \times 100 = 40°C \]

3. **Temperature of the Liquid**:
Since the thermometer indicates a rise of 40°C, this means the temperature of the warm liquid is:
\[ T = 40°C \]

4. **Convert Celsius to Kelvin**:
To convert the temperature from Celsius to Kelvin, we use the formula:
\[ T(K) = T(°C) + 273.15 \]
Substituting the value we found:
\[ T(K) = 40 + 273.15 = 313.15 K \]

### Final Answers:
- Temperature of the liquid in °C: **40°C**
- Temperature of the liquid in K: **313.15 K**