The molar heat capacity at constant pressure $C_p$ (in $\text{J mol}^{-1} K^{-1}$) for $n$-pentane as a function of temperature $(T$ in $K)$ is given by
$ \dfrac{C_p}{R} = 2.46 + 45.4 \times 10^{-3}T – 14.1 \times 10^{-6}T^2$. Take $R=8.314 \text{ J mol}^{-1} K^{-1}$.
At $1000 \: K$, the rate of change of molar entropy of $n$-pentane with respect to temperature at constant pressure is ______ $\text{J mol}^{-1} K^{-2}$ (round off to $2$ decimal places).