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. $C_{p}$ 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

\frac{C_{P} - C_{V}}{C_{V}}

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\frac{C_{P}}{C_{V}}

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\frac{C_{V}}{C_{p}}

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\frac{C_{p} - C_{v}}{C_{p}}

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Solution

The correct option is C $\frac{C_{V}}{C_{p}}$

If $V = C$
$T d s = d u + p d v$
$T d s = d u$
$d u = C_{v} d T$ [ $∵$ V = C]
$T d s = C_{v} d T$
${(\frac{d T}{d s})}_{V} = \frac{T}{C_{V}}$
If $P = C$
$T d s - d h - v d P$
$d h = C_{p} d T$ $[∵ P = C]$
$T d s = C_{p} d T$
${(\frac{d T}{d s})}_{p} = \frac{T}{C_{P}}$
Ratio, $\frac{(d T / d S)_{P}}{(d T / d S)_{V}}$

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Similar questions

γ = \frac{C_{p}}{C_{v}}

C_{p} =

C_{v} =

\frac{C_{p}}{C_{v}}

(C_{p})

(C_{v})

[C_{p} / C_{v}]

C_{p}

T = T_{0} + α V

T_{0}

α

C_{p}

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