A laboratory thermometer gave the reading of `-1^@C and 99^@C` when inserted into melting ice and boiling water respectively, both at standard atmospheric pressure. What is the error when the same thermometer is used to measure the difference between two arbitrary temperatures?

Options

A. `-1^@C`
B. `1^@C`
C. `0^@C`
D. `2^@C`

Explanation

To solve the problem, we need to determine the error in the temperature difference measured by the laboratory thermometer when it is used to measure the difference between two arbitrary temperatures.

### Step-by-Step Solution:

1. **Identify the Readings of the Thermometer:**
- The thermometer reads `-1°C` when measuring the melting ice (theoretical value is `0°C`).
- The thermometer reads `99°C` when measuring the boiling water (theoretical value is `100°C`).

2. **Determine the Errors in the Readings:**
- For melting ice:
- The actual temperature is `0°C`, but the thermometer reads `-1°C`.
- Error in melting ice = Actual temperature - Measured temperature = `0°C - (-1°C) = 1°C`.
- For boiling water:
- The actual temperature is `100°C`, but the thermometer reads `99°C`.
- Error in boiling water = Actual temperature - Measured temperature = `100°C - 99°C = 1°C`.

3. **Calculate the Difference Between the Two Readings:**
- The measured difference using the thermometer is:
- Measured difference = Reading at boiling water - Reading at melting ice = `99°C - (-1°C) = 99°C + 1°C = 100°C`.

4. **Calculate the Actual Difference:**
- The actual difference between the two temperatures is:
- Actual difference = Actual boiling point - Actual melting point = `100°C - 0°C = 100°C`.

5. **Determine the Error in the Difference Measurement:**
- Since both readings have the same error of `1°C`, when calculating the difference, these errors cancel each other out.
- Therefore, the error in the measured difference is:
- Error in difference = Measured difference - Actual difference = `100°C - 100°C = 0°C`.

### Conclusion:
The error when the same thermometer is used to measure the difference between two arbitrary temperatures is `0°C`.