Below Is a Table of the Vapor Pressure (In Kilopascals)

Essay

Below is a table of the vapor pressure (in kilopascals) of water for various temperatures (in degrees Kelvin): $$\begin{array} { | l | c | c | c | c | c | c | c | c | c | c | c | } \hline \text { Pressure } ( \mathrm { kPa } ) & 4.6 & 9.2 & 17.5 & 31.8 & 55.3 & 92.5 & 149.4 & 233.7 & 355.1 & 525.8 & 760 \\\hline \text { Temperature } \left( { } ^ { \circ } \mathrm { K } \right) & 273 & 283 & 293 & 303 & 313 & 323 & 333 & 343 & 353 & 363 & 373 \\\hline\end{array}$$ (a) Estimate the rate of change of pressure with respect to temperature on the following intervals:
(i) [363, 373]
(ii) [333, 343]
(iii) [273, 283]
(b) Plot the points from the table and fit an appropriate exponential model to these data.(c) From the model in part (b), determine the instantaneous rate of change of pressure with respect to temperature.(d) Is the rate of change of pressure increasing or decreasing with respect to temperature? Justify your answer.