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: Understanding the Question:
The question asks us to calculate the decrease in temperature on the Celsius scale when the temperature of boiling water is lowered to a point where a Fahrenheit thermometer reads $131^\circ\text{F}$.

Step 2: Key Formula and Approach:
We use the temperature conversion formula between the Celsius ($C$) and Fahrenheit ($F$) scales:
\[ \frac{C}{5} = \frac{F - 32}{9} \] We will find the initial and final temperatures on the Celsius scale to determine the temperature drop.

Step 3: Detailed Explanation:

• Initial State:
The thermometers are initially placed in boiling water.
The boiling point of water is:
\[ C_{\text{initial}} = 100^\circ\text{C} \] \[ F_{\text{initial}} = 212^\circ\text{F} \]

• Final State:
The final temperature on the Fahrenheit scale is:
\[ F_{\text{final}} = 131^\circ\text{F} \] Convert this temperature to the Celsius scale:
\[ C_{\text{final}} = \frac{5}{9} \left( F_{\text{final}} - 32 \right) \] \[ C_{\text{final}} = \frac{5}{9} \left( 131 - 32 \right) \] \[ C_{\text{final}} = \frac{5}{9} \times 99 = 5 \times 11 = 55^\circ\text{C} \]

• Calculate the Fall in Temperature ($\Delta C$):
The temperature drop measured by the Celsius thermometer is:
\[ \Delta C = C_{\text{initial}} - C_{\text{final}} \] \[ \Delta C = 100^\circ\text{C} - 55^\circ\text{C} = 45^\circ\text{C} \]

Step 4: Final Answer:
The fall in temperature as registered by the Celsius thermometer is $45^\circ$, which corresponds to Option (A).