Which of the following thermodynamic relation is incorrect?

T d s = C_{v} d T + T {(\frac{δ P}{δ T})}_{v} d v

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T d s = C_{p} d T - T {(\frac{δ v}{δ T})}_{p} d p

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C_{p} - C_{v} = \frac{T v^{2} β}{k_{T}}

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C_{p} - C_{v} = \frac{T v β^{2}}{k_{T}}

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Solution

The correct option is C $C_{p} - C_{v} = \frac{T v^{2} β}{k_{T}}$
$β = \frac{1}{v} {(\frac{δ c}{δ T})}_{P}$

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Which of the following relation is incorrect?

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