JEE Main 2022 · 30 June · morning · Single correct · +4 / −1

The pressure of the gas in a constant volume gas thermometer is 100 cm of mercury when placed in melting ice at 1 atm. When the bulb is placed in a liquid, the pressure becomes 180 cm of mercury. Temperature of the liquid is :
(Given 0°C = 273 K)

  1. (a) 300 K
  2. (b) 400 K
  3. (c) 600 K
  4. (d) 491 K
Answer and solution

Answer (d) 491 K

Solution

Physics sir · 3 steps

At constant volume, pressure is proportional to kelvin temperature, so scale 273 K by the pressure ratio.

  1. Constant volume. In a constant volume gas thermometer the gas obeys P ∝ T, with T in kelvin. So the ratio of pressures equals the ratio of absolute temperatures.

    T_(liquid)/T_(ice) = P_(liquid)/P_(ice)

  2. Put in numbers. Melting ice is at 273 K, where the pressure is 100 cm of Hg. So T_(liquid) = 273 × 180/100 = 491.4 K.
  3. So. The liquid is at about 491 K, which is option (d).

The idea to keep. Gas thermometers work in kelvin: pressure is proportional to absolute temperature. Always convert to kelvin before you take the ratio, never use degrees Celsius.

Answer from the NTA final answer key. Solution by PrepWiser.

Study Thermometry & Calorimetry

Asked about 50 times in JEE Main since 2020. This question is from 2022.