The Celsius and Fahrenheit scales are related by the formula
The Correct Answer and Explanation is:
Correct Answer:
The Celsius and Fahrenheit temperature scales are related by the formula:F=95C+32F = \frac{9}{5}C + 32F=59C+32
or alternatively,C=59(F−32)C = \frac{5}{9}(F – 32)C=95(F−32)
Explanation:
The Celsius and Fahrenheit scales are both used to measure temperature, but they are based on different reference points and increments. The Celsius scale is based on the freezing and boiling points of water at standard atmospheric pressure, where water freezes at 0 degrees Celsius and boils at 100 degrees Celsius. The Fahrenheit scale, on the other hand, places the freezing point of water at 32 degrees Fahrenheit and the boiling point at 212 degrees Fahrenheit.
To understand how the formula linking Celsius and Fahrenheit was developed, observe that the interval between freezing and boiling on the Celsius scale is 100 degrees, while on the Fahrenheit scale it is 180 degrees. This gives a ratio of 180:100, which simplifies to 9:5. This ratio shows that every increase of 1 degree Celsius corresponds to an increase of 1.8 degrees Fahrenheit.
The offset of 32 in the formula accounts for the difference in the zero points between the two scales. While 0 degrees Celsius is the freezing point of water, the equivalent in Fahrenheit is 32 degrees. Therefore, to convert Celsius to Fahrenheit, you first multiply the Celsius temperature by 9/5 to scale the temperature difference, and then add 32 to shift the baseline.
For example, to convert 25°C to Fahrenheit:F=95×25+32=45+32=77°FF = \frac{9}{5} \times 25 + 32 = 45 + 32 = 77°FF=59×25+32=45+32=77°F
To go the other way and convert 77°F to Celsius:C=59(77−32)=59×45=25°CC = \frac{5}{9}(77 – 32) = \frac{5}{9} \times 45 = 25°CC=95(77−32)=95×45=25°C
This consistent mathematical relationship allows accurate temperature conversion between the two scales.
