Water is placed in a container that is open to the atmosphere. (a) Determine the temperature and the vapor pressure at the boiling point at 0 ft above sea level. (b) Determine the temperature and the vapor pressure at the boiling point at 20,000 ft above sea level. (c) Discuss the results.

Question

Accepted Answer

The boiling point of a liquid is defined as the temperature at which the vapor pressure of the liquid equals to the pressure above it. Thus, if the water is placed in a container that is open to the atmosphere, then the water will boil at the temperature at which the vapor pressure of the water is equal to the atmospheric pressure.

(a) The atmospheric pressure at 0 ft above sea level is read from Table A.1 in Appendix A as follows:

[latex]P_{atm }=14.6959 psia [/latex]

Thus, the vapor pressure at the boiling point is equal to the atmospheric pressure as follows:

[latex] P_{\upsilon }=P_{atm }=14.6959 psia [/latex]

Reading from Table A.2 in Appendix A, this magnitude of vapor pressure for water occurs at a temperature of [latex]212^{\circ } F[/latex]. Thus, the temperature of water at the boiling point is [latex]212^{\circ } F[/latex].

(b) The atmospheric pressure at 20,000ft above sea level is read from Table A.1 in Appendix A as follows:

[latex] P_{atm }=6.7588psia [/latex]

Thus, the vapor pressure at the boiling point is equal to the atmospheric pressure as follows:

[latex]P_{\upsilon } = P_{atm } =6.7588 psia[/latex]

Reading from Table A.2 in Appendix A, this magnitude of vapor pressure for water occurs at a temperature of roughly [latex]175^{\circ } F[/latex]. Thus, the temperature of water at the boiling point is roughly [latex]175^{\circ } F[/latex].

Therefore, because the atmospheric pressure decreases with an increase in altitude, the corresponding vapor pressure, [latex]P_{\upsilon } = P_{atm } [/latex] at the boiling point also decreases. Furthermore, because the vapor pressure decreases with a decrease in temperature (graphically illustrated in Example Problem 1.33 above), the corresponding boiling point will also decrease.

Table A.1
Physical Properties for the International Civil Aviation Organization (ICAO) Standard Atmosphere as a Function of Elevation above Sea Level
Elevation above Sea Level ft	Temperature (θ) [latex]^{\circ } F[/latex]	Absolute Pressure (p) psia	Density [latex]\left( ho ight) [/latex] [latex]slug/ft^{3} [/latex]	Specific Weight [latex]\left(\gamma ight) [/latex] [latex]lb/ft^{3} [/latex]	Absolute (Dynamic) Viscosity [latex]\left(\mu ight) [/latex] [latex]10^{-6} lb - sec/ft^{2} [/latex]	Kinematic Viscosity (ν) [latex]10^{-3} ft^{2}/sec [/latex]	Speed of Sound (c) ft/sec	Acceleration due to Gravity (g) [latex]ft/sec^{2} [/latex]
0	59.000	14.69590	0.002376800	0.0764720	0.37372	0.15724	1116.45	32.174
5000	41.173	12.22830	0.002048100	0.0658640	0.36366	0.17756	1097.08	32.158
10.000	23.355	10.10830	0.001755500	0.0564240	0.35343	0.20133	1077.40	32.142
15.000	5.545	8.29700	0.001496100	0.0480680	0.34302	0.22928	1057.35	32.129
20.000	-12.255	6.75880	0.001267200	0.0406940	0.33244	0.26234	1039.94	32.113
25.000	-30.048	5.46070	0.001066300	0.0342240	0.32166	0.30167	1016.11	32.097
30.000	-47.048	4.37260	0.000890650	0.0285730	0.31069	0.34884	994.85	32.081
35.000	-65.607	3.46760	0.000738190	0.0236720	0.29952	0.40575	973.13	32.068
40.000	-69.700	2.73000	0.000587260	0.0188230	0.29691	0.50559	968.08	32.052
45.000	-69.700	2.14890	0.000462270	0.0148090	0.29691	0.64230	968.08	32.036
50.000	-69.700	1.69170	0.000363910	0.0116520	0.29691	0.81589	968.08	32.020
60.000	-69.700	1.04880	0.000225610	0.0072175	0.29691	1.31600	968.08	31.991
70.000	-67.425	0.65087	0.000139200	0.0044485	0.29836	2.14340	970.90	31.958
80.000	-61.976	0.40632	0.000085707	0.0027366	0.30182	3.52150	997.62	31.930
90.000	-56.535	0.25540	0.000053145	0.0016950	0.30525	5.74360	984.28	31.897
100.000	-51.099	0.16160	0.000033182	0.0010575	0.30865	9.30180	990.91	31.868
Elevation above Sea Level Km	Temperature (θ) [latex]^{\circ } C[/latex]	Absolute Pressure (p) kPa abs	Density [latex]\left( ho ight) [/latex] [latex]kg/m^{3} [/latex]	Specific Weight [latex]\left(\gamma ight) [/latex] [latex]N/m^{3} [/latex]	Absolute (Dynamic) Viscosity [latex]\left(\mu ight) [/latex] [latex]10^{-6} N - sec/m^{2} [/latex]	Kinematic Viscosity (ν) [latex]10^{-6} m^{2}/sec [/latex]	Speed of Sound (c) m/sec	Acceleration due to Gravity (g) [latex]m/sec^{2} [/latex]
0	15.000	101.325	1.22500	12.0131	17.894	14.607	340.294	9.80665
1	8.501	89.876	1.11170	10.8987	17.579	15.813	336.430	9.80360
2	2.004	79.501	1.00660	9.8652	17.260	17.147	332.530	9.80050
3	-4.500	70.121	0.90925	8.9083	16.938	18.628	328.580	9.78740
4	-10.984	61.66	0.81935	8.0250	16.612	20.275	324.590	9.79430
5	-17.474	54.048	0.73643	7.2105	16.282	22.110	320.550	9.79120
6	-23.693	47.217	0.66011	6.4613	15.949	24.161	316.450	9.78820
8	-36.935	35.651	0.52579	5.1433	15.271	29.044	308.110	9.78000
10	-49.898	26.499	0.41351	4.0424	14.577	35.251	299.530	9.77590
12	-56.500	19.399	0.31194	3.0476	14.216	45.574	295.070	9.76970
14	-56.500	14.17	0.22786	2.2247	14.216	62.391	295.070	9.76360
16	-56.500	10.352	0.16647	1.6243	14.216	85.397	295.070	9.75750
18	-56.500	7.565	0.12165	1.1862	14.216	116.860	295.070	9.75130
20	-56.500	5.529	0.08891	0.8664	14.216	159.890	295.070	9.74520
25	-51.598	2.549	0.04008	0.3900	14.484	361.350	298.390	9.73000
30	-46.641	1.197	0.01841	0.1788	14.753	801.340	301.710	7.71470

Table A.2
Physical Properties for Water at Standard Sea-Level Atmospheric Pressure as a Function of Temperature
Temperature (θ) [latex]^{\circ } F[/latex]	Density (ρ) [latex]slug/ft^{3} [/latex]	Specific Weight (γ) [latex]Ib/ft^{3}[/latex]	Absolute (Dynamic) Viscosity (μ) [latex]10^{-6} Ib-sec/ft^{3}[/latex]	Kinematic Viscosity (ν) [latex]10^{-6} ft^{2}/sec[/latex]	Surface Tension (σ) lb=ft	Vapor Pressure [latex]( ho _{ u } )[/latex] psia	Bulk Modulus of Elasticity [latex](E_{\upsilon } )[/latex] psi
32	1.940	62.42	37.46	19.31	0.00518	0.0885	293.000
40	1.940	62.43	32.29	16.64	0.00514	0.1220	294.000
50	1.940	62.41	27.35	14.10	0.00509	0.1780	305.000
60	1.938	62.37	23.59	12.17	0.00504	0.2560	311.000
70	1.936	62.30	20.50	10.59	0.00498	0.3630	320.000
80	1.934	62.22	17.99	9.30	0.00492	0.5070	322.000
90	1.931	62.11	15.95	8.26	0.00486	0.6980	323.000
100	1.927	62.00	14.24	7.39	0.00480	0.9490	327.000
110	1.923	61.86	12.84	6.67	0.00473	1.2750	331.000
120	1.918	61.71	11.68	6.09	0.00467	1.6920	333.333
130	1.913	61.55	10.69	5.58	0.00460	2.2200	334.000
140	1.908	61.38	9.81	5.14	0.00454	2.8900	330.000
150	1.902	61.20	9.05	4.76	0.00447	3.7200	328.000
160	1.896	61.00	8.38	4.42	0.00441	4.7400	326.000
170	1.890	60.80	7.80	4.13	0.00434	5.9900	322.000
180	1.883	60.58	8.26	3.85	0.00427	7.5100	318.000
190	1.876	60.36	6.78	3.62	0.00420	9.3400	313.000
200	1.868	60.12	6.37	3.41	0.00413	11.5200	308.000
212	1.860	59.83	5.93	3.19	0.00404	14.6900	300.000
[latex]^{\circ } C[/latex]	[latex]kg/m^{3} [/latex]	[latex]KN/m^{3} [/latex]	[latex]N-sec/m^{2} [/latex]	[latex]10^{-6} m^{2} /sec[/latex]	[latex]N/m[/latex]	[latex]KN/m^{2} abs[/latex]	[latex]10^{6} KN/m^{2} [/latex]
0	999.8	9.805	0.001781	1.785	0.0756	0.6110	2.02
5	1000.0	9.807	0.001518	1.519	0.0749	0.872	2.06
10	999.7	9.804	0.001307	1.306	0.0742	1.230	2.10
15	999.1	9.798	0.001139	1.139	0.0735	1.710	2.14
20	998.2	9.789	0.001002	1.003	0.0725	2.340	2.18
25	997.0	9.777	0.000890	0.893	0.0720	3.170	2.22
30	995.7	9.765	0.000798	0.800	0.0712	4.240	2.25
40	992.2	9.731	0.000653	0.659	0.0696	7.380	2.28
50	988.0	9.690	0.000547	0.553	0.0697	12.330	2.29
60	983.2	9.642	0.000466	0.474	0.0662	19.920	2.28
70	977.8	9.589	0.000404	0.413	0.0644	31.160	2.25
80	971.8	9.530	0.000356	0.364	0.0626	47.340	2.20
90	965.3	9.467	0.000315	0.326	0.0608	70.100	2.14
100	958.4	9.399	0.000282	0.294	0.0589	101.330	2.07

Question 1.34: Water is placed in a container that is open to the atmospher...

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