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Question 2.SP.11: At approximately what temperature will water boil if the ele......

At approximately what temperature will water boil if the elevation is  10,000 ft  ?

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From Appendix A, Table A.3, the pressure of the standard atmosphere at 10 000-ft elevation is 10.11 psia. From Appendix A, Table A.1, the saturationvapor pressure  p_v   of water is 10.11 psia at about 193°F (by interpolation). Hence the water at 10,000 ft will boil at about 193°F.

Compared with the boiling temperature of  212° F at sea level, this explains why it takes longer to cook at high elevations.

TABLE A.1  Physical properties of water at standard sea-level atmospheric pressure   { }^a
Temperature,  Specific weight, Density, Absolute viscosity {}^b Kinematic viscosity, {}^b Surface tension, Saturation vapor pressure, Satur’n vapor pressure head, Bulk  modulus  of  elasticity,
  \boldsymbol{T}    \boldsymbol{\gamma}    \boldsymbol{\rho}   \boldsymbol{ \mu}   \boldsymbol{\nu}    \boldsymbol{\sigma} \boldsymbol{ p_v} \boldsymbol{ p_v}/ \boldsymbol{\gamma} \boldsymbol{E_v}
  { }^{\circ} \mathbf{F}     \mathbf{l b} / \mathbf{f t}^3   \boldsymbol{ slugs/ft { }^3}   10^{-6} \mathbf{lb} \cdot \mathrm{sec} / \mathbf{ft}^2   10^{-6} \mathbf{ft}^2 / \mathbf{sec} \mathbf{lb} / \mathbf{ft} psia ft abs psi
32  { }^{\circ} \mathrm{F} 62.42 1.940 37.46 19.31 0.00518 0.0885 0.204 293,000
40  { }^{\circ} \mathrm{F} 62.43 1.940 32.29 16.64 0.00514 0.122 0.281 294,000
50  { }^{\circ} \mathrm{F} 62.41 1.940 27.35 14.10 0.00509 0.178 0.411 305,000
60  { }^{\circ} \mathrm{F} 62.37 1.938 23.59 12.17 0.00504 0.256 0.592 311,000
70  { }^{\circ} \mathrm{F} 62.30 1.936 20.50 10.59 0.00498 0.363 0.839 320,000
80  { }^{\circ} \mathrm{F} 62.22 1.934 17.99 9.30 0.00492 0.507 1.173 322,000
90  { }^{\circ} \mathrm{F} 62.11 1.931 15.95 8.26 0.00486 0.698 1.618 323,000
100  { }^{\circ} \mathrm{F} 62.00 1.927 14.24 7.39 0.00480 0.949 2.20 327,000
110  { }^{\circ} \mathrm{F} 61.86 1.923 12.84 6.67 0.00473 1.275 2.97 331,000
120  { }^{\circ} \mathrm{F} 61.71 1.918 11.68 6.09 0.00467 1.692 3.95 333,000
130  { }^{\circ} \mathrm{F} 61.55 1.913 10.69 5.58 0.00460 2.22 5.19 334,000
140  { }^{\circ} \mathrm{F} 61.38 1.908 9.81 5.14 0.00454 2.89 6.78 330,000
150  { }^{\circ} \mathrm{F} 61.20 1.902 9.05 4.76 0.00447 3.72 8.75 328,000
160  { }^{\circ} \mathrm{F} 61.00 1.896 8.38 4.42 0.00441 4.74 11.18 326,000
170  { }^{\circ} \mathrm{F} 60.80 1.890 7.80 4.13 0.00434 5.99 14.19 322,000
180  { }^{\circ} \mathrm{F} 60.58 1.883 7.26 3.85 0.00427 7.51 17.84 318,000
190  { }^{\circ} \mathrm{F} 60.36 1.876 6.78 3.62 0.00420 9.34 22.28 313,000
200  { }^{\circ} \mathrm{F} 60.12 1.868 6.37 3.41 0.00413 11.52 27.59 308,000
212  { }^{\circ} \mathrm{F} 59.83 1.860 5.93 3.19 0.00404 14.69 35.36 300,000
{ }^{\circ} \mathbf{C}   \mathbf{kN} / \mathbf{m}^3   \mathbf{~kg} / \mathbf{m}^3   \mathbf{~N} \cdot \mathbf{s} / \mathbf{m}^2   10^{-6} \mathbf{~m}^2 / \mathbf{s} \mathbf{N} / \mathbf{m}   \mathbf{kN} / \mathbf{m}^2 \text { abs }    \mathbf{m} \text { abs }    10^6 \mathbf{kN} / \mathbf{m}^2
0  { }^{\circ} \mathrm{C} 9.805 999.8 0.001781 1.785 0.0756 0.611 0.0623 2.02
5  { }^{\circ} \mathrm{C} 9.807 1000.0 0.001518 1.519 0.0749 0.872 0.0889 2.06
10  { }^{\circ} \mathrm{C} 9.804 999.7 0.001307 1.306 0.0742 1.230 0.1255 2.1
15  { }^{\circ} \mathrm{C} 9.798 999.1 0.001139 1.139 0.0735 1.710 0.1745 2.14
20  { }^{\circ} \mathrm{C} 9.789 998.2 0.001002 1.003 0.0728 2.34 0.239 2.18
25  { }^{\circ} \mathrm{C} 9.777 997.0 0.000890 0.893 0.072 3.17 0.324 2.22
30  { }^{\circ} \mathrm{C} 9.765 995.7 0.000798 0.800 0.0712 4.24 0.434 2.25
40  { }^{\circ} \mathrm{C} 9.731 992.2 0.000653 0.658 0.0696 7.38 0.758 2.28
50  { }^{\circ} \mathrm{C} 9.690 988.0 0.000547 0.553 0.0679 12.33 1.272 2.29
60  { }^{\circ} \mathrm{C} 9.642 983.2 0.000466 0.474 0.0662 19.92 2.07 2.28
70  { }^{\circ} \mathrm{C} 9.589 977.8 0.000404 0.413 0.0644 31.16 3.25 2.25
80  { }^{\circ} \mathrm{C} 9.530 971.8 0.000354 0.364 0.0626 47.34 4.97 2.2
90  { }^{\circ} \mathrm{C} 9.467 965.3 0.000315 0.326 0.0608 70.10 7.40 2.14
100  { }^{\circ} \mathrm{C} 9.399 958.4 0.000282 0.294 0.0589 101.33 10.78 2.07
{ }^a In these tables, if (for example, at 32^{\circ} \mathrm{F} ) \mu is given as 37.46 and the units are 10^{-6} \mathrm{lb} \cdot \mathrm{sec} / \mathrm{ft}^2 then \mu=37.46 \times 10^{-6} \mathrm{lb} \cdot \mathrm{sec} / \mathrm{ft}^2.
{ }^b {\text {For viscosity, see also Figs. A.1 and A.2. }}.

 

TABLEA.3 The ICAO  {}^a    standard atmosphere  {}^b
  \textbf { Elevation above sea level }      \textbf { Temperature }  \\ T    \textbf { Absolute pressure }  \\  p    \textbf { Specific weight } \\ \gamma    \textbf { Density, }   \\ \rho    \textbf { Absolute viscosity } \\ \mu    \textbf { Kinematic viscosity } \\\nu \textbf { Speed of sound }  \\ c   \textbf { Gravitational acceleration } \\ g
  \mathbf{ft}   { }^{\circ} \mathbf{F}   \mathbf{psia}   \mathbf{lb} / \mathbf{ft}^3   \mathbf{sl} / \mathbf{ug} / \mathbf{ft}^3    10^{-6} \mathbf{lb} \cdot \mathbf{sec} / \mathbf{ft}^2   10^{-3} \mathbf{ft}^2 / \mathbf{sec}   \mathbf{ft} / \mathbf{sec}   \mathbf{ft} / \mathbf{sec}^2
0 59.000 14.6959 0.076472 0.0023768 0.37372 0.15724 1116.45 32.1740
5,000 41.173 12.2283 0.065864 0.0020481 0.36366 0.17756 1097.08 32.158
10,000 23.355 10.1083 0.056424 0.0017555 0.35343 0.20133 1077.4 32.142
15,000 5.545 8.2970 0.048068 0.0014961 0.34302 0.22928 1057.35 32.129
20,000 -12.255 6.7588 0.040694 0.0012672 0.33244 0.26234 1036.94 32.113
25,000 -30.048 5.4607 0.034224 0.0010663 0.32166 0.30167 1016.11 32.097
30,000 -47.832 4.3726 0.028573 0.00089065 0.31069 0.34884 994.85 32.081
35,000 -65.607 3.4676 0.023672 0.00073819 0.29952 0.40575 973.13 32.068
40,000 -69.700 2.7300 0.018823 0.00058726 0.29691 0.50559 968.08 32.052
45,000 -69.700 2.1489 0.014809 0.00046227 0.29691 0.6423 968.08 32.036
50,000 -69.700 1.6917 0.011652 0.00036391 0.29691 0.81589 968.08 32.020
60,000 -69.700 1.0488 0.007218 0.00022561 0.29691 1.3160 968.08 31.991
70,000 -67.425 0.6509 0.004449 0.0001392 0.29836 2.1434 970.9 31.958
80,000 -61.976 0.4063 0.002737 0.000085707 0.30182 3.5215 977.62 31.930
90,000 -56.535 0.2554 0.001695 0.000053145 0.30525 5.7436 984.28 31.897
100,000 -51.099 0.1616 0.001058 0.000033182 0.30865 9.3018 990.91 31.868
  \mathbf{km} { }^{\circ} \mathbf{C} \mathbf{kPa} a b s \mathbf{~N} / \mathbf{m}^3 \mathbf{~kg} / \mathbf{m}^3 10^{-6} \mathbf{~N} \cdot \mathbf{s} / \mathbf{m}^2 10^{-6} \mathbf{~m}^2 / \mathbf{s} \mathbf{m} / \mathbf{s} \mathbf{m} / \mathbf{s}^2
0 15.000 101.325 12.0131 1.2250 17.894 14.607 340.294 9.80665
1 8.501 89.876 10.8987 1.1117 17.579 15.813 336.43 9.8036
2 2.004 79.501 9.8652 1.0066 17.260 17.147 332.53 9.8005
3 -4.500 70.121 8.9083 0.90925 16.938 18.628 328.58 9.7974
4 -10.984 61.66 8.0250 0.81935 16.612 20.275 324.59 9.7943
5 -17.474 54.048 7.2105 0.73643 16.282 22.110 320.55 9.7912
6 -23.963 47.217 6.4613 0.66011 15.949 24.161 316.45 9.7882
8 -36.935 35.651 5.1433 0.52579 15.271 29.044 308.11 9.7820
10 -49.898 26.499 4.0424 0.41351 14.577 35.251 299.53 9.7759
12 -56.500 19.399 3.0476 0.31194 14.216 45.574 295.07 9.7697
14 -56.500 14.170 2.2247 0.22786 14.216 62.391 295.07 9.7636
16 -56.500 10.352 1.6243 0.16647 14.216 85.397 295.07 9.7575
18 -56.500 7.565 1.1862 0.12165 14.216 116.86 295.07 9.7513
20 -56.500 5.529 0.8664 0.08891 14.216 159.89 295.07 9.7452
25 -51.598 2.549 0.3900 0.04008 14.484 361.35 298.39 9.7300
30 -46.641 1.197 0.1788 0.01841 14.753 801.34 301.71 9.7147
a International Civil Aviation Organization; see Sec. 2.9.
b In these tables, if (for example, at 0 \mathrm{ft} ) \mu is given as 0.37372 and the units are 10^{-6} \mathrm{lb} \cdot \mathrm{sec} / \mathrm{ft}^2 then \mu=0.37372 \times 10^{-6} \mathrm{lb} \cdot \mathrm{sec} / \mathrm{ft}^2
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A2_917590

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