NDA (II) 2018 General Ability Test · Question 89 of 146

Correct — C, −273·15 °C. The Kelvin and Celsius scales use degrees of exactly the same size; they differ only in where the zero is placed. Celsius fixes its zero at the melting point of ice, while the Kelvin scale fixes its zero at absolute zero, the temperature at which the thermal motion of particles is at its irreducible minimum and a gas would have no pressure left to exert. The offset between the two zeros is 273·15 degrees, so the conversion is simply K = °C + 273·15, and setting K to zero gives °C = −273·15.

• (a)0 °C — This is the melting point of ice, which is 273·15 K — the zero of the Celsius scale, not the zero of the Kelvin scale. Assuming that two scales with the same size of degree must also share a zero is exactly the confusion the question is testing.
• (b)–100 °C — A round number with nothing behind it. It corresponds to 173·15 K, a temperature that is cold but perfectly ordinary — carbon dioxide is solid there and liquid nitrogen is still far colder.
• (d)–173·15 °C — The near-miss designed to catch a student converting with 173 instead of 273. It equals 100 K, which is a real and reachable temperature; there is nothing special about it, and 100 K is not the bottom of the scale.

Absolute zero is not merely the coldest temperature yet reached but the lower bound of the temperature scale itself. It emerges from the gas laws: extrapolating the straight-line plot of the pressure or volume of an ideal gas against temperature, both would fall to zero at −273·15 °C. Nothing can be colder, because there is no less thermal energy to have. Lord Kelvin proposed building a thermodynamic scale on that point, and the resulting kelvin is one of the seven base units of the SI system. Since the 2019 redefinition the kelvin has been fixed through the Boltzmann constant rather than through the triple point of water, but the numerical relation to Celsius is unchanged.

Two things make this question easy to get wrong under time pressure. The first is that all four options are numbers of the same shape, so a student who remembers only 'about two hundred and something below zero' can be pulled to 173·15. The second is the sign — absolute zero is far below the Celsius zero, so the answer must be negative. Note also the convention the paper follows correctly: kelvin temperatures are written without a degree symbol, as 0 K rather than 0 °K, because the scale is absolute rather than relative to an arbitrary fixed point.

• The conversion between the two scales is K = °C + 273·15, so absolute zero is −273·15 °C.
• A degree Celsius and a kelvin are the same size, so temperature differences are numerically identical on the two scales.
• Absolute zero is the temperature at which an ideal gas would exert no pressure; it is unattainable in practice.
• The kelvin is an SI base unit and is written without a degree sign — 300 K, not 300 °K.

• Converting with 173 instead of 273 — the single most common slip on this question.
• Forgetting the minus sign; absolute zero lies far below the freezing point of water.
• Writing kelvin temperatures with a degree symbol. The correct form is 0 K.

NDA asks for a temperature converted between scales, for the value of absolute zero, or for the lowest temperature among a set of options.

• practice — not a real PYQ

  A temperature of 27 °C expressed on the Kelvin scale is

  • (a)246 K
  • (b)273 K
  • (c)300 K
  • (d)327 K

  Answer(c) 300 K — add 273 to the Celsius reading, since the two scales differ only in where the zero sits.

• practice — not a real PYQ

  The volume of a fixed mass of an ideal gas at constant pressure, plotted against temperature in °C, extrapolates to zero at

  • (a)0 °C
  • (b)−100 °C
  • (c)−273·15 °C
  • (d)−373·15 °C

  Answer(c) −273·15 °C — this extrapolation is what locates absolute zero in the first place.