Question

A Celsius and a Fahrenheit thermometers are dipped in boiling water. The water temperature is lowered until the Fahrenheit thermometer registers $131^\circ$. The fall in temperature as registered by the Celsius thermometer is:

• A. $45^\circ$
• B. $40^\circ$
• C. $60^\circ$
• D. $75^\circ$

Hint:

A change of $9$ divisions on the Fahrenheit scale is equivalent to a change of $5$ divisions on the Celsius scale.
Using the ratio $\Delta C = \frac{5}{9} \Delta F$, we can calculate:
$\Delta F = 212 - 131 = 81^\circ\text{F}$, so
$\Delta C = \frac{5}{9} \times 81 = 45^\circ\text{C}$.
This approach is faster and avoids full scale conversions.

Answer 1

The Correct Option is A

Step 1: Work with the change directly, not the full scale.
Since 100 Celsius degrees span the same physical range as 180 Fahrenheit degrees, every $9$ Fahrenheit degrees correspond to $5$ Celsius degrees, so $\Delta C = \frac{5}{9}\Delta F$.
Step 2: Find how much the Fahrenheit reading fell.
Boiling water reads $212^\circ\text{F}$, and it fell to $131^\circ\text{F}$, so \[ \Delta F = 212-131 = 81^\circ\text{F} \]
Step 3: Convert that drop to Celsius using the ratio. \[ \Delta C = \frac{5}{9}\times81 = 45^\circ\text{C} \]
\[ \boxed{\Delta C = 45^\circ\text{C}} \]