
Derive a relation between the Celsius and Fahrenheit scales of temperature using the fixed point in two different scales.
Answer
485.4k+ views
Hint: We know that the two scales used for temperature measurements are Celsius and Fahrenheit. We also know that the temperature in the centigrade scale will be expressed in degrees Celsius. So, we find the relationship and then derive the above statement to correct two separate scales.
Formula used:
Celsius to Fahrenheit,
Fahrenheit to Celsius,
Where,
is the temperature in Fahrenheit,
is the temperature on the centigrade scale.
Complete step-by-step solution:
Given by,
The relation between the Celsius and Fahrenheit scales,
The Celsius-Fahrenheit relationship is direct. Celsius is specifically linked to Fahrenheit.
Which suggests that
As the temperature rises on the Celsius scale, the equivalent temperature of Fahrenheit would also be high.
As the temperature falls on the Celsius scale, the temperature equal to Fahrenheit would also be low.
Here, we define,
is Lower Fixed Point
is Upper Fixed Point
According to that,
On simplifying,
We get,
Again, we resolve the above equation,
We get,
A temperature scale based on the freezing point of water at and the boiling point of water at is the Celsius scale, or centigrade scale. The Fahrenheit scale is a temperature scale based on the water freezing point and the water boiling point.
Hence,
Thus, the Celsius and Fahrenheit scales of temperature using the fixed point in two different scales
Note: The above derivation is evaluating the relation between Celsius and Fahrenheit is proportional. Both have different freezing points of water and both follow the varied unit difference between each scale. That is because of the Celsius temperature scale, part of the metric system that denotes the temperature.
Formula used:
Celsius to Fahrenheit,
Fahrenheit to Celsius,
Where,
Complete step-by-step solution:
Given by,
The relation between the Celsius and Fahrenheit scales,
The Celsius-Fahrenheit relationship is direct. Celsius is specifically linked to Fahrenheit.
Which suggests that
As the temperature rises on the Celsius scale, the equivalent temperature of Fahrenheit would also be high.
As the temperature falls on the Celsius scale, the temperature equal to Fahrenheit would also be low.
Here, we define,
According to that,
On simplifying,
We get,
Again, we resolve the above equation,
We get,
A temperature scale based on the freezing point of water at
Hence,
Thus, the Celsius and Fahrenheit scales of temperature using the fixed point in two different scales
Note: The above derivation is evaluating the relation between Celsius and Fahrenheit is proportional. Both have different freezing points of water and both follow the varied unit difference between each scale. That is because of the Celsius temperature scale, part of the metric system that denotes the temperature.
Latest Vedantu courses for you
Grade 8 | CBSE | SCHOOL | English
Vedantu 8 CBSE Pro Course - (2025-26)
School Full course for CBSE students
₹45,300 per year
Recently Updated Pages
Master Class 11 Economics: Engaging Questions & Answers for Success

Master Class 11 Accountancy: Engaging Questions & Answers for Success

Master Class 11 English: Engaging Questions & Answers for Success

Master Class 11 Social Science: Engaging Questions & Answers for Success

Master Class 11 Physics: Engaging Questions & Answers for Success

Master Class 11 Biology: Engaging Questions & Answers for Success

Trending doubts
How many moles and how many grams of NaCl are present class 11 chemistry CBSE

How do I get the molar mass of urea class 11 chemistry CBSE

Define least count of vernier callipers How do you class 11 physics CBSE

Plants which grow in shade are called A Sciophytes class 11 biology CBSE

A renewable exhaustible natural resource is A Petroleum class 11 biology CBSE

In which of the following gametophytes is not independent class 11 biology CBSE
