NDA (I) 2017 General Ability Test · Question 121 of 149

Correct — B, 301. Let the Celsius reading be C. The Kelvin reading is then K = C + 273 and the Fahrenheit reading is F = (9/5)C + 32. The question says the two thermometers show the same number, so set them equal: C + 273 = 1.8C + 32. Collecting terms gives 273 − 32 = 1.8C − C, that is 241 = 0.8C, so C = 301.25, which rounds to 301. Check it: at C = 301.25 the Kelvin reading is 574.25 and the Fahrenheit reading is 1.8 × 301.25 + 32 = 574.25 as well, so the two do coincide. Using 273.15 instead of 273 shifts the answer only to about 301.4, so the option is unaffected.

• (a)574 — This is the number the Kelvin and Fahrenheit thermometers themselves show at that temperature, which is exactly the value the question does not ask for. It is the most attractive distractor precisely because the working produces it as a by-product; the Celsius reading is that number minus 273.
• (c)273 — This is a reflex answer, borrowed from the fact that 0 °C equals 273 K. It is a conversion constant, not a solution of the equation the question sets up.
• (d)232 — No correct step in either conversion produces this number. It is placed as a plain wrong value for a candidate who guesses at the size of the answer instead of solving for it.

Three scales are in common use and they differ in two ways — where the zero sits and how large one degree is. Celsius sets zero at the ice point and 100 at the steam point. Kelvin keeps the same size of degree but shifts the zero down to absolute zero, so K = C + 273.15. Fahrenheit shifts the zero and shrinks the degree, with 180 Fahrenheit degrees spanning the same interval as 100 Celsius degrees, which is where the 9/5 comes from. Every conversion question in this family is solved by writing the two expressions and setting them equal.

Two coincidences are worth memorising, because papers use both. The Celsius and Fahrenheit scales read the same number at minus forty degrees, and the Kelvin and Fahrenheit scales read the same at about 574.6. This question uses the second coincidence but then asks for something one step beyond it — the Celsius value at that same temperature — and plants the coincidence value itself as option (a). The general lesson for numerical items of this kind is to finish the question that was asked; the number that falls out midway through the algebra is very often on the option list as a trap.

• The Kelvin and Celsius scales are related by K = C + 273.15 and share the same size of degree.
• The Fahrenheit and Celsius scales are related by F = (9/5)C + 32.
• The Celsius and Fahrenheit scales read the same number at −40 degrees.
• The Kelvin and Fahrenheit scales read the same number at about 574.6, which corresponds to about 301.4 °C.

• Answering with the value the two matching thermometers show instead of the value asked for.
• Writing K = C − 273 or F = (5/9)C + 32 and inverting a conversion.
• Assuming the answer must be a familiar constant such as 273 or −40.

NDA asks for a straight conversion between scales, or for the temperature at which two scales read alike.

• practice — not a real PYQ

  At what temperature do the Celsius and Fahrenheit scales show the same numerical reading?

  • (a)0 degrees
  • (b)−40 degrees
  • (c)32 degrees
  • (d)100 degrees

  Answer(b) −40 degrees — setting C = 1.8C + 32 gives C = −40, the one point where the two scales coincide.

• practice — not a real PYQ

  A temperature of 37 °C expressed on the Kelvin scale is about

  • (a)273 K
  • (b)300 K
  • (c)310 K
  • (d)347 K

  Answer(c) 310 K — add 273 to the Celsius reading, which is why normal body temperature is quoted as about 310 K.