JEE Main 2023 · 29 January · morning · Single correct · +4 / −1

A bicycle tyre is filled with air having pressure of 270 kPa at 27° C. The approximate pressure of the air in the tyre when the temperature increases to 36° C is

  1. (a) 262 kPa
  2. (b) 360 kPa
  3. (c) 270 kPa
  4. (d) 278 kPa
Answer and solution

Answer (d) 278 kPa

Solution

Physics sir · 3 steps

The tyre volume barely changes, so pressure goes up in step with temperature, but only in kelvin.

  1. Fixed volume. The amount of air and the tyre's volume stay the same. From PV = nRT, P is then proportional to T, so P₂/P₁ = T₂/T₁.
  2. Convert to kelvin. T₁ = 27 + 273 = 300 K and T₂ = 36 + 273 = 309 K.

    P₂ = P₁ × T₂/T₁ = 270 × 309/300 kPa = 278.1 kPa

  3. So. The pressure rises to about 278 kPa, which is option (d).

The idea to keep. Gas laws only work with absolute temperature. Always add 273 before taking any ratio of temperatures.

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

Study Kinetic Theory of Gases

Asked about 130 times in JEE Main since 2020. This question is from 2023.