Question

A celsius and a Fahrenheit thermometer are dipped in boiling water. The temperature of water is lowered until the Farenheit thermometer shows \(140^{\circ}\). What is the fall in temperature on the Celsius thermometer?

• A. \(60^{\circ}\) C
• B. \(40^{\circ}\) C
• C. \(50^{\circ}\) C
• D. \(80^{\circ}\) C

Hint:

Boiling water is 100 C or 212 F. Convert the fall in Fahrenheit degrees into Celsius degrees using the ratio 5 to 9.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
A Celsius degree is larger than a Fahrenheit degree. The scales are linked by \(\dfrac{C}{5} = \dfrac{F - 32}{9}\), so a change of 9 F equals a change of 5 C.

Step 2: Find the fall in F.
Boiling water is at \(212^\circ\)F. It cools to \(140^\circ\)F, so the fall is \(212 - 140 = 72\) F degrees.

Step 3: Convert.
\[ \Delta C = \frac{5}{9}\times 72 = 40 \]

Step 4: Check the options.
60, 50 and 80 degrees do not match. A common slip is to use \(\dfrac{9}{5}\) in place of \(\dfrac{5}{9}\).

Final Answer:
The fall in temperature on the Celsius thermometer is \(40^\circ\)C, option (B). \[ \boxed{40^{\circ}\text{C}} \]