For an ideal gas, a constant pressure line and a constant volume line intersect at a point, in the Temperature $(T)$ versus specific entropy $\text{(s)}$ diagram. $C_{P}$ is the specific heat at constant pressure and $C_{V}$ 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

1. $\dfrac{C_{P}-C_{V}}{C_{P}} \\$
2. $\dfrac{C_{P}}{C_{V}} \\$
3. $\dfrac{C_{P}-C_{V}}{C_{V}} \\$
4. $\dfrac{C_{V}}{C_{P}}$

Ans- D

In the TS plane

(dT/dS)p = T/Cp ….(1)

(dT/dS)v = T/Cv…..(2) [ T/Cv >T/Cp, this is why constant volume slope is steeper than const. pressure slope in TS plane]

(1)/(2)= Cv/Cp

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