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Chapter 8: Problem 1091

A Centigrade and a Fahrenheit thermometer are dipped in boiling water. The water temperature is lowered until the Fahrenheit thermometer registered \(140^{\circ} .\) What is the fall in thermometers (A) \(80^{\circ}\) (B) \(60^{\circ}\) (C) \(40^{\circ}\) (D) \(30^{\circ}\)

Short Answer

Expert verified
The fall in temperature is approximately \(22.22^{\circ}C\) which is not available in the given options. This means none of the options provided are correct for the given exercise.

Step by step solution

01

Calculate the fall in Fahrenheit temperature

Given that the water started at boiling point, and the boiling point of water in Fahrenheit is \(212^{\circ}F\). The temperature falls to \(140^{\circ}F\) as per the given exercise. So, the fall in Fahrenheit temperature would be: \(Fall_{F} = Initial_{F} - Final_{F}\)
02

Substitute the values and find the fall in Fahrenheit temperature

The initial temperature is \(212^{\circ}F\) and the final temperature is \(140^{\circ}F\). Now we substitute the values into the formula and find the temperature fall: \(Fall_{F} = 212^{\circ} - 140^{\circ} = 72^{\circ}\)
03

Convert Fahrenheit to Centigrade using the conversion formula

Now, we know that the fall in Fahrenheit temperature is \(72^{\circ}F\). We will convert this to Centigrade using the Fahrenheit-Centigrade conversion formula: \(C = \frac{5}{9}(F-32)\) Before we move to the next step, let's represent the fall in Fahrenheit temperature as \(Fall_C\), which we want to find using the above formula.
04

Substitute the values and solve for the fall in temperature in Centigrade

Now, substituting the values and solving for the fall temperature in Centigrade: \(Fall_{C} = \frac{5}{9}(72-32)\) \(Fall_{C} = \frac{5}{9}(40)\) \(Fall_{C} = \frac{200}{9} = 22.22^{\circ}\) Now, let's compare this temperature fall with the options given in the exercise: (A) \(80^{\circ}\) (B) \(60^{\circ}\) (C) \(40^{\circ}\) (D) \(30^{\circ}\) The temperature fall we found in Centigrade is approximately \(22.22^{\circ}C\), which is not available in the given options. This means none of the options provided are correct for the given exercise.

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