JEE Main 2023 · 24 January · evening · Single correct · +4 / −1

In an Isothermal change, the change in pressure and volume of a gas can be represented for three different temperature; T₃ > T₂ > T₁ as :

  1. (a)
    Option (a)
  2. (b)
    Option (b)
  3. (c)
    Option (c)
  4. (d)
    Option (d)
Answer and solution

Answer (b)

Solution

Physics sir · 3 steps

Check two things in each graph: is the isotherm a hyperbola, and is the hottest curve farthest from the axes?

  1. Shape of an isotherm. For an ideal gas at fixed temperature, PV = nRT is a constant. So P ∝ 1/V, and the curve is a rectangular hyperbola, not a straight line.

    PV = nRT = constant for each isotherm

  2. Order of the curves. A higher temperature gives a larger value of PV. At the same volume the hotter gas has a higher pressure, so its curve lies farther from the origin. Since T₃ > T₂ > T₁, the T₃ curve must be outermost and the T₁ curve innermost.
    OptionShapeOutermost curveVerdict
    (a)hyperbolaT₁wrong order
    (b)hyperbolaT₃correct
    (c)straight lineT₁wrong shape and order
    (d)straight lineT₃wrong shape
  3. So. Only (b) shows hyperbolic isotherms with T₃ farthest from the origin, then T₂, then T₁ closest.

The idea to keep. On a P-V graph, isotherms are hyperbolas PV = nRT. The hotter the gas, the bigger the product PV, so the curve sits farther out from both axes.

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

Study Thermodynamics

Asked about 150 times in JEE Main since 2020. This question is from 2023.