In a mercury thermometer the ice point (lower fixed point) is marked as 10° and the steam point (upper fixed point) is marked as 130°. At 40°C temperature, what will this thermometer read? A. 78° B. 66° C. 62° D. 58°

To find out what the thermometer will read at 40°C, we need to first understand how the mercury thermometer is calibrated. In this particular thermometer, the ice point is marked at 10° and the steam point at 130°. This means that the temperature range it measures is between these two points, which is 120° (130° - 10°). The key is to map the actual temperature to this scale.

Steps to Calculate the Reading

Here’s how to determine the reading at 40°C:

• Identify the actual temperature range: The actual range from 0°C to 100°C is equivalent to a range of 120° on the thermometer scale, between 10° and 130°.
• Find the difference from the ice point: The ice point is 10°C, so from 0°C to 40°C, we have a difference of 40°C - 0°C = 40°C.
• Determine the fraction of the range: The actual range (0°C to 100°C) is 100°C. The thermometer has a range of 120°, so the fraction of the range that corresponds to 40°C is:
• Calculating the thermometer reading: Since the thermometer starts at 10°, we add the fraction of the range that corresponds to 40°C to this point. The scaled temperature can be calculated using the formula:

Formula for Conversion

The formula to convert the temperature is:

Temperature on thermometer = Ice Point + (Actual Temperature × (Thermometer Range / Actual Range))

Plugging in the values:

Actual Temperature = 40°C

Ice Point = 10°

Thermometer Range = 120° (from 10° to 130°)

Actual Range = 100°C (from 0°C to 100°C)

Using the formula:

Temperature on thermometer = 10° + (40 × (120 / 100))

Temperature on thermometer = 10° + (40 × 1.2)

Temperature on thermometer = 10° + 48°

Temperature on thermometer = 58°

Final Reading

Thus, at 40°C, the thermometer will read 58°. Therefore, the correct answer is D. 58°.

Understanding how to scale temperature readings on a non-standard thermometer is crucial, especially in practical applications where traditional benchmarks may not apply. Always remember to carefully identify the calibration points and apply the appropriate conversions. This skill can come in handy in various scientific and everyday contexts!