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Thermodynamics
Entropy & Second Law
GATE 2020
Medium

For an ideal gas, a constant pressure line and a constant volume line intersect at a point, in the Temperature (T) versus specific entropy (s) diagram. Cp is the specific heat at constant pressure and Cv is the specific heat at constant volume. The ratio of the slopes of the constant pressure and constant volume lines at the point of intersection is

  • A(Cp−Cv)/Cp
  • BCp/Cv
  • C(Cp−Cv)/Cv
  • Cv/Cp

Explanation

At constant p, Tds=CpdT so (dT/ds)_p = T/Cp. At constant v, Tds=CvdT so (dT/ds)_v = T/Cv. The ratio of the constant-pressure slope to the constant-volume slope is (T/Cp)/(T/Cv) = Cv/Cp.

Source: GATE ME 2020 Session 1 (ME-1) (2020)

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