The GATE Grind

GATE 2020 ME (ME1) – Question 28

Thermodynamics · Entropy changes, closed and open systems · 1 mark · Multiple choice

For an ideal gas, a constant-pressure line and a constant-volume line intersect on a temperature T versus specific entropy s diagram. $C_p$ and $C_v$ are specific heats at constant pressure and volume. Find the ratio of slopes of the constant-pressure and constant-volume lines at their intersection.

  1. $(C_p-C_v)/C_p$
  2. $C_p/C_v$
  3. $(C_p-C_v)/C_v$
  4. $C_v/C_p$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (D) $C_v/C_p$

Explanation

At constant pressure ds=Cp dT/T, giving dT/ds=T/Cp. At constant volume the slope is T/Cv. At their common temperature the ratio is **Cv/Cp, D**. The ratio is less than one because Cp>Cv.