JEE Main 2020 · 8 January · morning · Single correct · +4 / −1

A thermodynamic cycle xyzx is shown on a V-T diagram.
The P-V diagram that best describes this cycle is :
(Diagrams are schematic and not to scale)

JEE Main PYQ figure
  1. (a)
    Option (a)
  2. (b)
    Option (b)
  3. (c)
    Option (c)
  4. (d)
    Option (d)
Answer and solution

Answer (a)

Solution

Physics sir · 4 steps

Read each leg of the V-T graph as a process first, then draw those same three processes on P-V.

  1. Leg x to y. This line passes through the origin, so V ∝ T. For an ideal gas PV = nRT, which means P is constant. So x to y is an isobaric expansion, because both V and T rise.
  2. Leg y to z. y to z is horizontal, so V stays fixed while T falls. That is an isochoric step, and P drops.
  3. Leg z to x. z to x is vertical, so T stays fixed while V falls. That is an isothermal compression, and P rises along a hyperbola PV = constant.
    LegProcessShape on P-V
    x to yP constant, V increaseshorizontal line, moving right
    y to zV constant, P decreasesvertical line, moving down
    z to xT constant, V decreasesrising hyperbola, moving left
  4. So. Only (a) shows a horizontal x to y at high pressure, a vertical drop from y to z, and a curved isotherm from z back up to x. The answer is (a).

The idea to keep. On a V-T graph, a line through the origin means constant pressure, a horizontal line means constant volume, and a vertical line means constant temperature. Name each leg first, then sketch it on P-V.

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 2020.