# Why is the equation for Entropy of an ideal gas that undergoes reversible change in T at constant Pressure like this?

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.