Problem 11.50

Appendix B lists the vapor pressure of water at various external pressures.

(a) Plot the data in Appendix B, vapor pressure (torr) vs. temperature (oC). From your plot, estimate the vapor pressure of water at body temperature, 37oC.

OK, look up the data, fire up excel, and plot it (I'll be looking for your plot when you turn your homework in.)

Here it is....

To estimate the vapor pressure at 37 oC, either look on the plot or look at the data in Appendix B. You should get about 49 torr.

(b)Explain the significance of the data point at 760.0 torr, 100 oC.

This is the normal boiling point of water - if 1 atm pressure is exerted on the water, its vapor pressure will equal 760 torr when it's temperature is 100 oC.

(c) A city at an altitude of 5000 ft above sea level would have a barometric pressure of 633 torr. To what temperature would you have to heat water to boil it in this city?

Looking at our plot and/or the data, we want the temperature for which the vapor pressure = 633 torr. This will be at about 95 oC.

(d) A city at an altitude 500 ft below sea level would have an atmospheric pressure of 774 torr. To what temperature would you have to heat water to boil it in this city?

Again, looking at our plot: we fix atmoshperic pressure to 774 torr, and find the temperature to be around 101 oC.

(e) For the two cities in parts (c) and (d), compare the average kinetic energies of the water molecules at their boiling points. Are the kinetic energies the same or different? Explain.

At 5000 ft above sea level the water boils at about 95 oC, while 500 ft below sea level the water boils at around 101 oC. Recall from kinetic-molecular theory that average KE is directly proportional to absolute temperature. The water molecules at 101 oC have a higher average KE than the water molecules at 95 oC because they're at a higher temperature.