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Why is the equation for change in Entropy for a reversible change in $T$ at constant $P$ described as

$$\Delta S = n C_p \ln\frac{T_f}{T_i}$$

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Begin with $$ \delta Q = T dS $$ and recall that the heat transfer for an ideal gas at constant pressure is $$ \delta Q = nC_p dT $$ Combining these gives $$ dS = n C_p \frac{dT}{T} $$ and integrating both sides with respect to temperature from $T_i$ to $T_f$ gives $$ S_f - S_i = nC_p \ln\frac{T_f}{T_i} $$ as desired.

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