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

question 103

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.

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Definitions:

Ménière's Disease

A disorder of the inner ear characterized by episodes of vertigo, tinnitus, and hearing loss.

Otomycosis

A fungal infection of the ear, usually affecting the ear canal, characterized by pain, itchiness, and possible hearing loss.

Fenestration

A surgical procedure that creates an opening, especially used in ear surgery to restore hearing.

Eustachian

Pertains to the Eustachian tube, a canal that connects the middle ear to the nasopharynx, which helps equalize air pressure on both sides of the eardrum.