If a thermometer reads freezing point of water as 20°C and boiling point as 150°C, how much thermome

If a thermometer reads freezing point of water as 20°C and boiling point as 150°C, how much thermometer read when the actual temperature is 60°C?
(a) 98°C
(b) 10°C
(c) 40°C
(d) 60°C
Certainly! Let’s briefly discuss how to relate the readings of a thermometer to actual temperature scales when given a thermometer with an unconventional calibration.

Understanding Thermometer Calibration

Thermometers can be calibrated to different scales, and sometimes they do not directly align with the standard Celsius or Fahrenheit scales. Calibration determines how a thermometer's readings correspond to actual temperatures.

Calibration Basics

1. *Thermometer Calibration Points:*
Thermometers are often calibrated using fixed points such as the freezing and boiling points of water. For example, a thermometer might be calibrated so that the freezing point of water corresponds to a specific reading on the thermometer.

2. *Linear Calibration:*
If a thermometer's readings are linearly related to actual temperatures, you can find a simple linear equation to convert between the thermometer’s scale and the actual temperature scale. This involves determining:
- The range of temperatures the thermometer covers.
- The corresponding readings for known temperatures (e.g., freezing and boiling points).

3. *Deriving the Conversion Formula:*
With the known calibration points, you derive a linear equation of the form:
\[
T_{\text{thermo}} = a \times T_{\text{actual}} + b
\]
where:
- \(T_{\text{thermo}}\) is the temperature reading on the thermometer.
- \(T_{\text{actual}}\) is the actual temperature in the standard scale.
- \(a\) and \(b\) are constants determined from the calibration points.

Applying the Calibration

Once the linear equation is established, you can use it to find the thermometer reading for any given actual temperature. Simply plug the actual temperature into the equation to get the corresponding thermometer reading.

Practical Applications

- *Scientific Measurements:* Accurate calibration is crucial for experiments requiring precise temperature measurements.
- *Everyday Use:* In cooking or weather forecasting, understanding how a thermometer’s readings relate to standard temperature scales ensures correct interpretation and adjustments.

In summary, calibrating a thermometer involves setting reference points and deriving a linear relationship to convert its readings to actual temperatures. This process is essential for ensuring accuracy in various applications where precise temperature measurements are needed.
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