In a mercury rhermometer the ice point (lower fixed point) is marked as `10^(@)` and the steam point (upper fixed point ) is marked as `130^(@).` At `40^(@)C` tmperature, what will this thermometer read?

Options

A. `78^(@)`
B. `66^(@)`
C. `62^(@)`
D. `58^(@)`

Explanation

To find the reading of the mercury thermometer at a temperature of \(40^\circ C\), we can use the concept of linear interpolation between the two fixed points (ice point and steam point).

### Step-by-Step Solution:

1. **Identify the Fixed Points**:
- Ice point (lower fixed point) is marked as \(10^\circ C\).
- Steam point (upper fixed point) is marked as \(130^\circ C\).

2. **Determine the Range**:
- The range of the thermometer is from \(10^\circ C\) to \(130^\circ C\).
- The total range is \(130 - 10 = 120^\circ C\).

3. **Calculate the Temperature Difference**:
- The temperature difference from the ice point to the given temperature \(40^\circ C\) is:
\[ 40 - 10 = 30^\circ C \]

4. **Find the Fraction of the Range**:
- The fraction of the range from the ice point to the given temperature is:
\[ \frac{30}{120} = \frac{1}{4} \]

5. **Calculate the Corresponding Reading on the Thermometer**:
- We need to find the equivalent reading \(T\) on the thermometer scale. The formula to find this is:
\[ T = \text{Lower Fixed Point} + \left(\frac{\text{Difference from Lower Fixed Point}}{\text{Total Range}}\right) \times (\text{Upper Fixed Point} - \text{Lower Fixed Point}) \]
- Plugging in the values:
\[ T = 10 + \left(\frac{30}{120}\right) \times (130 - 10) \]
- Simplifying:
\[ T = 10 + \left(\frac{1}{4}\right) \times 120 \]
\[ T = 10 + 30 = 40 \]

6. **Final Calculation**:
- The thermometer reading at \(40^\circ C\) is:
\[ T = 10 + 30 = 40^\circ C \]

### Conclusion:
The thermometer will read \(40^\circ C\) at the actual temperature of \(40^\circ C\).