Chapter 3, Problem 1P

Because the pressure falls, water boils at a lower temperature with increasing altitude. Consequently, cake mixes and boiled eggs, among other foods, must be cooked different lengths of time. Determine the boiling temperature of water at 1000 and 2000 m elevation on a standard day, and compare with the sea-level value.

To determine

The boiling temperature of water at 1000 and 2000 m elevation.

Explanation of Solution

Determine the atmospheric pressure at the given altitudes from Table A.3, Appendix A.

Elevation (m)	$\left(\frac{p}{p_0}\right)$	$p\left(\text{kPa}\right)$
0	1	101.3
1000	0.887	89.6
2000	0.7846	79.3

Check the steam tables for the variation of saturation temperature with pressure.

$p\left(\text{kPa}\right)$	$T_{sat}^{*}\left(°\text{C}\right)$
70	90
80	93.5
90	96.7
101.3	100.0

Interpolate the data for elevation 1000 m.

  $\begin{array}{l}\frac{p_1-p_2}{T_1-T_2}=\frac{p_3-p_1}{T_3-T_1}\\ \frac{80\text{ kPa}-89.6\text{ kPa}}{93.5°\text{C}-T_{@1000\text{ m}}}=\frac{90\text{ kPa}-80\text{ kPa}}{96.7°\text{C}-93.5°\text{C}}\\ T_{@1000\text{ m}}=96.6°\text{C}\end{array}$

Interpolate the data for elevation 2000 m.

  $\begin{array}{l}\frac{p_1-p_2}{T_1-T_2}=\frac{p_3-p_1}{T_3-T_1}\\ \frac{80\text{ kPa}-79.3\text{ kPa}}{93.5°\text{C}-T_{@2000\text{ m}}}=\frac{70\text{ kPa}-80\text{ kPa}}{90°\text{C}-93.5°\text{C}}\\ T_{@2000\text{ m}}=93.2°\text{C}\end{array}$

Write the data to correlate saturation temperature with altitude.

Elevation (m)	$\left(\frac{p}{p_0}\right)$	$p\left(\text{kPa}\right)$	$T_{sat}^{*}\left(°\text{C}\right)$
0	1	101.3	100
1000	0.887	89.6	96.6
2000	0.7846	79.3	93.2

The saturation temperature drops about $\underset{\_}{3.4°\text{C}/\text{1000 m}}$.