The GATE Grind

GATE 2024 AE – Question 18

Propulsion · Basics of thermodynamics · 1 mark · Multiple choice

In the figure shown below, various thermodynamics processes for an ideal gas are represented. Match each curve with the process that it best represents.

A temperature against entropy plot with five lines through one point. A horizontal line $aa'$, a vertical line $bb'$, and two rising curves through the point: $cc'$ (dashed) and $dd'$ (solid), where $dd'$ is steeper than $cc'$.
  1. $aa'$ – Isentropic; $bb'$ – Isothermal; $cc'$ – Isobaric; $dd'$ – Isochoric
  2. $aa'$ – Isothermal; $bb'$ – Isentropic; $cc'$ – Isochoric; $dd'$ – Isobaric
  3. $aa'$ – Isothermal; $bb'$ – Isentropic; $cc'$ – Isobaric; $dd'$ – Isochoric
  4. $aa'$ – Isothermal; $bb'$ – Isobaric; $cc'$ – Isentropic; $dd'$ – Isochoric

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Correct answer: (C) $aa'$ – Isothermal; $bb'$ – Isentropic; $cc'$ – Isobaric; $dd'$ – Isochoric

Explanation

On a $T$-$s$ diagram a horizontal line is constant temperature (isothermal) and a vertical line is constant entropy (isentropic). For the two rising curves, the slope is $\frac{dT}{ds} = \frac{T}{c}$, which is $\frac{T}{c_p}$ for an isobar and $\frac{T}{c_v}$ for an isochore. As $c_v < c_p$, the isochore is the steeper one ($dd'$) and the isobar the flatter one ($cc'$).