Appendix \(\mathrm{B}\) lists the vapor pressure of water at various external pressures. (a) Plot the data in Appendix B,vapor pressure versus temperature $\left({ }^{\circ} \mathrm{C}\right) .$ From your plot, estimate the vapor pressure of water at body temperature, \(37^{\circ} \mathrm{C}\). (b) Explain the significance of the data point at $101.3 \mathrm{kPa}, 100^{\circ} \mathrm{C} .(\mathbf{c}) \mathrm{A}\( city at an altitude of \)1525 \mathrm{~m}$ above sea level has a barometric pressure of \(84.3 \mathrm{kPa}\). To what temperature would you have to heat water to boil it in this city? (d) A city at an altitude of \(150 \mathrm{~m}\) below sea level would have a barometric pressure of \(103.14 \mathrm{kPa}\). To what temperature would you have to heat water to boil it in this city?

Short Answer

Expert verified
(a) By plotting the data in Appendix B and estimating from the graph, the vapor pressure of water at body temperature (\(37^{\circ} \mathrm{C}\)) is approximately \(6.3 \mathrm{kPa}\). (b) The data point at \(101.3 \mathrm{kPa}, 100^{\circ} \mathrm{C}\) represents the standard boiling point of water at sea level, since the external pressure is equal to the standard atmospheric pressure. (c) In a city at an altitude of \(1525 \mathrm{~m}\) above sea level with a barometric pressure of \(84.3 \mathrm{kPa}\), water would boil at approximately \(95^{\circ} \mathrm{C}\) based on the graph. (d) In a city at an altitude of \(150 \mathrm{~m}\) below sea level with a barometric pressure of \(103.14 \mathrm{kPa}\), water would boil at approximately \(101^{\circ} \mathrm{C}\) based on the graph.

Step by step solution

01

(a) Estimate the vapor pressure of water at body temperature

To do this, follow these steps: 1. Plot the data from Appendix B on graph paper or use software to create the graph. On the x-axis, plot the temperature in °C and on the y-axis, plot the vapor pressure in kPa. 2. Use a smooth curve to connect the points and estimate the vapor pressure of water at \(37^{\circ} \mathrm{C}\). The graph should resemble an increasing curve with a relatively smooth shape.
02

(b) Significance of the data point at \(101.3 \mathrm{kPa}, 100^{\circ} \mathrm{C}\)

At this data point, the external pressure is equal to the standard atmospheric pressure (\(101.3 \mathrm{kPa}\)). At this pressure, water boils at \(100^{\circ} \mathrm{C}\). This data point represents the standard boiling point of water at sea level.
03

(c) Boiling temperature of water at \(1525 \mathrm{~m}\) above sea level

To find the boiling temperature of water at this altitude, follow these steps: 1. Use the given barometric pressure, \(84.3 \mathrm{kPa}\), as the external pressure. 2. Locate the external pressure on the y-axis of the previously plotted graph. Find the corresponding temperature on the x-axis. 3. This temperature is the boiling point of water in a city at an altitude of \(1525 \mathrm{~m}\) above sea level.
04

(d) Boiling temperature of water at \(150 \mathrm{~m}\) below sea level

To find the boiling temperature of water at this altitude, follow these steps: 1. Use the given barometric pressure, \(103.14 \mathrm{kPa}\), as the external pressure. 2. Locate the external pressure on the y-axis of the previously plotted graph. Find the corresponding temperature on the x-axis. 3. This temperature is the boiling point of water in a city at an altitude of \(150 \mathrm{~m}\) below sea level.

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