Final answer:
The temperature range of the thermometer is 225.0 K, from 498.0 K to 273.0 K. The total uncertainty is ± 0.75 K, resulting from adding the high and low-end uncertainties of ± 0.5 K and ± 0.25 K, respectively.
Step-by-step explanation:
The temperature range of a thermometer that reads from 498 ± 0.5K to 273 ± 0.25K can be found by subtracting the lower limit of the higher temperature from the higher limit of the lower temperature. The result is the maximum extent of the range. Uncertainty in this context is the absolute error in the temperature readings given by the thermometer.
To find the temperature range:
- Highest temperature reading = 498.0 K
- Lowest temperature reading = 273.0 K
- Temperature range = Highest temperature - Lowest temperature = 498.0 K - 273.0 K = 225.0 K
To find the total uncertainty, we add the uncertainties at the high and low end:
- Highest temperature uncertainty = ± 0.5 K
- Lowest temperature uncertainty = ± 0.25 K
- Total uncertainty = 0.5 K + 0.25 K = ± 0.75 K
This means that any temperature measurement within this range could be off by up to ± 0.75 K. In real-world connections, such as when checking for a fever, having a thermometer with minimal uncertainty is crucial for reliable measurements.