Which of the following is a correct relationship between Fahrenheit (°F) and Celsius (°C) degrees ?

Question

UnlockIAS · Accepted Answer

Correct — C, °F = (9/5) °C + 32. The relation between two linear temperature scales is fixed entirely by two reference points. At standard atmospheric pressure water freezes at 0 °C and 32 °F, and boils at 100 °C and 212 °F. So the same interval that is 100 degrees wide on the Celsius scale is 212 − 32 = 180 degrees wide on the Fahrenheit scale, which makes one Celsius degree equal to 180/100 = 9/5 = 1.8 Fahrenheit degrees. That ratio 9/5 is the multiplier, and because Fahrenheit's zero sits 32 of its own degrees below the freezing point of water, 32 must be added afterwards. Putting the two together gives °F = (9/5) °C + 32, which is option (c) and the marked answer. Check it against both anchors: put °C = 0 and you get 32 °F, the freezing point; put °C = 100 and you get 180 + 32 = 212 °F, the boiling point. Rearranging the same equation gives the inverse, °C = (5/9)(°F − 32) — note that the 32 is subtracted first and only then scaled, which is the step candidates most often get wrong. Two arithmetic checkpoints are worth memorising because they let you verify any version of this formula in seconds: normal human body temperature is 37 °C = 98.6 °F, and the two scales cross at −40, where −40 °C is exactly −40 °F.

Why the other options are wrong — (a) The right formula written backwards — it has the correct multiplier and the correct constant but swaps which scale is being converted into which. Test it on a known point and it collapses at once: the freezing point of water is 32 °F, and substituting °F = 32 gives °C = (9/5)(32) + 32 = 57.6 + 32 = 89.6 °C, whereas water plainly freezes at 0 °C. The genuine inverse is °C = (5/9)(°F − 32); going from Fahrenheit to Celsius you must subtract the 32 first and then multiply by 5/9, not multiply by 9/5 and then add. This is the most attractive wrong option in the set, because a candidate who has memorised the shape of the formula without memorising its direction has no way to choose between (a) and (c).  (b) This is the Celsius-to-Kelvin relation with the wrong scale written into it. The number 273.15 belongs to the absolute or Kelvin scale: K = °C + 273.15, so °C = K − 273.15. Fahrenheit has nothing to do with 273.15; its corresponding absolute scale is the Rankine scale, whose offset is 459.67. Test the option on the boiling point of water, 212 °F, and it gives °C = 212 − 273.15 = −61.15 °C, when the correct value is 100 °C. The option works as a distractor only on a candidate who remembers the figure 273.15 but not which pair of scales it connects.  (d) The same misuse of 273.15 as option (b), simply written in the other direction, and it fails just as fast. Substituting the freezing point of water, °C = 0, gives °F = −273.15, whereas water freezes at 32 °F. It is also wrong in a way that should be visible without any arithmetic: any correct Celsius-to-Fahrenheit formula must contain a scaling factor, because the two scales have different degree sizes, and this option has none at all — it only shifts the number without stretching it.

Concept: A temperature scale is defined by choosing a zero point and a degree size, so converting between any two linear scales always takes the same two-step form: multiply by the ratio of the degree sizes, then shift by the difference in zeros. Celsius fixes 0 at the freezing point and 100 at the boiling point of water at standard atmospheric pressure. Fahrenheit puts those same two points at 32 and 212, so it has 180 degrees where Celsius has 100 and its degree is only 5/9 as large. Kelvin, the SI base unit of thermodynamic temperature, keeps the Celsius degree size but moves the zero down to absolute zero, so K = °C + 273.15 with no multiplier at all. Recognising which conversions need a multiplier and which need only an offset is what separates the correct option here from the two that misuse 273.15.

State PCS 2024 Q106 — Science & Technology PYQ with Answer

State PCS 2024 Q106 — Science & Technology PYQ with Answer