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Equipartition Theorem

Variation of ...

Question

Variation of heat of reaction with temperature is given by Kirchhoff's equation.Which of the following is not the equation for kirchhoff's ?

A

Δ H_{2} = Δ H_{1} + Δ C_{y} (T_{2} - T_{1})

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B

d H = T d S + V d P

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C

\frac{Δ H_{2} - Δ H_{1}}{Δ T} = Δ C_{p}

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D

\frac{d (Δ H)}{Δ T} = Δ C_{p}

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Solution

The correct option is B $d H = T d S + V d P$
Kirchoff's law describes the variation of enthalpy of a reaction with the change in temperature. And at constant pressure, if the heat capacities $(c_{p})$ do not vary with temperature then the change in enthalpy is a function of the difference in temperature and the heat capacities.
$Δ H_{2} = Δ H_{1} + Δ c_{p} (T_{2} - T_{1})$
So, equations $C$ and $D$ are the form of the above equation.
The equation $B) d H = T d S + V d P$ is derived from the second law of thermodynamics.

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