
A Celsius thermometer and a Fahrenheit thermometer are put in a hot bath. The reading on Fahrenheit thermometer is just 3 times the reading on Celsius thermometer. The temperature of the hot bath is
A) ${26.67^ \circ }\,C$
B) ${36.67^ \circ }\,C$
C) ${46.67^ \circ }\,C$
D) ${56.67^ \circ }\,C$
Answer
135k+ views
Hint:- The above given problem can be solved using the formula that is derived for the relationship between the Celsius thermometer and the Fahrenheit thermometer of the hot bath where the Fahrenheit thermometer is just 3 times the reading on Celsius thermometer.
Useful formula:
The formula for the relationship between Celsius and Fahrenheit;
$\dfrac{{F - 32}}{{180}} = \dfrac{C}{{100}}$
Where, $F$ denotes the value of Fahrenheit in the Fahrenheit scale, $C$ denotes the value of Celsius in the Celsius scale.
Complete step by step solution:
The data given in the problem is;
Reading on Fahrenheit thermometer is just 3 times the reading on Celsius thermometer, that is;
$F = 3C$
Therefore, the relationship between Celsius and Fahrenheit;
$\dfrac{{F - 32}}{{180}} = \dfrac{C}{{100}}$
$
\dfrac{{3C - 32}}{{100}} = \dfrac{C}{{100}} \\
C = \dfrac{{80}}{3} \\
$
On simplifying we get;
$C = {26.67^ \circ }\,C$.
Therefore, the temperature of the hot bath according to the Celsius thermometer is $C = {26.67^ \circ }\,C$.
Hence the option (A), $C = {26.67^ \circ }\,C$ is the correct answer.
Note: Since in the problem it is only asked to find the temperature of the water bath Celsius thermometer that in Celsius, we didn’t calculate the temperature of the water bath in Fahrenheit thermometer.
Useful formula:
The formula for the relationship between Celsius and Fahrenheit;
$\dfrac{{F - 32}}{{180}} = \dfrac{C}{{100}}$
Where, $F$ denotes the value of Fahrenheit in the Fahrenheit scale, $C$ denotes the value of Celsius in the Celsius scale.
Complete step by step solution:
The data given in the problem is;
Reading on Fahrenheit thermometer is just 3 times the reading on Celsius thermometer, that is;
$F = 3C$
Therefore, the relationship between Celsius and Fahrenheit;
$\dfrac{{F - 32}}{{180}} = \dfrac{C}{{100}}$
$
\dfrac{{3C - 32}}{{100}} = \dfrac{C}{{100}} \\
C = \dfrac{{80}}{3} \\
$
On simplifying we get;
$C = {26.67^ \circ }\,C$.
Therefore, the temperature of the hot bath according to the Celsius thermometer is $C = {26.67^ \circ }\,C$.
Hence the option (A), $C = {26.67^ \circ }\,C$ is the correct answer.
Note: Since in the problem it is only asked to find the temperature of the water bath Celsius thermometer that in Celsius, we didn’t calculate the temperature of the water bath in Fahrenheit thermometer.
Recently Updated Pages
JEE Main 2021 July 25 Shift 2 Question Paper with Answer Key

JEE Main 2021 July 25 Shift 1 Question Paper with Answer Key

JEE Main 2021 July 20 Shift 2 Question Paper with Answer Key

JEE Main 2021 July 22 Shift 2 Question Paper with Answer Key

How to find Oxidation Number - Important Concepts for JEE

Half-Life of Order Reactions - Important Concepts and Tips for JEE

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility, & More

JEE Main 2025: Derivation of Equation of Trajectory in Physics

Degree of Dissociation and Its Formula With Solved Example for JEE

A body is falling from a height h After it has fallen class 11 physics JEE_Main

Electric Field Due to Uniformly Charged Ring for JEE Main 2025 - Formula and Derivation

Elastic Collisions in One Dimension - JEE Important Topic

Other Pages
JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

Units and Measurements Class 11 Notes: CBSE Physics Chapter 1

Important Questions for CBSE Class 11 Physics Chapter 1 - Units and Measurement

NCERT Solutions for Class 11 Physics Chapter 2 Motion In A Straight Line

NCERT Solutions for Class 11 Physics Chapter 1 Units and Measurements

Motion In A Plane: Line Class 11 Notes: CBSE Physics Chapter 3
