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A 1-kg block of sub-zero ice is dropped into a large drum of cold water at 0 C. The drum is insulated from outside. Immediately after dropping it, you measured that the ice-block is gaining heat from the water at a rate of 126 W. How much time will it take for all the ice to melt? (no more information is required)

A 1-kg block of sub-zero ice is dropped into a large drum of cold water at 0 C. The drum is insulated from outside. Immediately after dropping it, you measured that the ice-block is gaining heat from the water at a rate of 126 W. How much time will it take for all the ice to melt? (no more information is required)

College Physics
College Physics
1st Edition
ISBN:9781938168000
Author:Paul Peter Urone, Roger Hinrichs
Publisher:Paul Peter Urone, Roger Hinrichs
Chapter13: Temperature, Kinetic Theory, And The Gas Laws
Section: Chapter Questions
Problem 50PE: (a) What is me vapor pressure of water at 20.0C ? (b) What percentage of atmospheric pressure does...
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A 1-kg block of sub-zero ice is dropped into a large drum of cold water at 0 C. The drum is insulated

from outside. Immediately after dropping it, you measured that the ice-block is gaining heat from

the water at a rate of 126 W. How much time will it take for all the ice to melt? (no more information is required)

 

 

Boiling and freezing point properties Substance Ammonia Argon Benzene Brine (20% sodium chloride by mass) n-Butane Carbon dioxide Ethanol Ethyl alcohol Ethylene glycol Glycerine Helium Hydrogen Isobutane Kerosene Mercury Methane Methanol Nitrogen Octane Oil (light) Oxygen Petroleum Propane Refrigerant-134a Water Boiling Data at I atm Normal Latent Heat of Boiling Point, °C -33.3 -185.9 80.2 103.9 -0.5 -78.4* 78.2 78.6 198.1 179.9 -268.9 -252.8 -11.7 204-293 356.7 -161.5 64.5 -195.8 124.8 -183 100 Vaporization hig, kJ/kg 1357 161.6 394 385.2 230.5 (at 0°C) 838.3 855 800.1 974 22.8 445.7 367.1 251 294.7 510.4 1100 230-384 427.8 216.8 2257 Freezing Data Freezing Point, °C -77.7 - 189.3 5.5 -17.4 -138.5 -56.6 -114.2 -156 -10.8 18.9 -259.2 - 160 -24.9 NOT FOR DIS -97.7 -210 -57.5 -218.8 -187.7 -96.6 0.0 Latent Heat of Fusion Temperature, Density hif, kJ/kg °C p, kg/m³ 322.4 28 126 80.3 109 108 181.1 200.6 59.5 105.7 11.4 58.4 99.2 25.3 180.7 13.7 80.0 333.7 -33.3 -20 0 25 -185.6 20 20 -0.5 0 25 20 20 20 -268.9 -252.8 -11.7 20 25 -161.5 -100 25 -195.8 - 160 20 25 - 183 20 -42.1 0 50 -50 -26.1 0 25 0 25 Liquid Properties 50 75 00 682 665 639 602 1394 879 1150 601 298 783 789 1109 1261 146.2 70.7 593.8 820 13,560 423 301 787 809 596 703 910 1141 640 581 529 449 1443 1374 1295 1207 1000 997 988 975 958 Specific Heat Cp, kJ/kg.K 4.43 4.52 4.60 4.80 1.14 1.72 3.11 2.31 0.59 2.46 2.84 2.84 2.32 22.8 10.0 2.28 2.00 0.139 3.49 5.79 2.55 2.06 2.97 2.10 1.80 1.71 2.0 2.25 2.53 3.13 1.23 1.27 1.34 1.43 4.22 4.18 4.18 4.19 4.22
Transcribed Image Text:Boiling and freezing point properties Substance Ammonia Argon Benzene Brine (20% sodium chloride by mass) n-Butane Carbon dioxide Ethanol Ethyl alcohol Ethylene glycol Glycerine Helium Hydrogen Isobutane Kerosene Mercury Methane Methanol Nitrogen Octane Oil (light) Oxygen Petroleum Propane Refrigerant-134a Water Boiling Data at I atm Normal Latent Heat of Boiling Point, °C -33.3 -185.9 80.2 103.9 -0.5 -78.4* 78.2 78.6 198.1 179.9 -268.9 -252.8 -11.7 204-293 356.7 -161.5 64.5 -195.8 124.8 -183 100 Vaporization hig, kJ/kg 1357 161.6 394 385.2 230.5 (at 0°C) 838.3 855 800.1 974 22.8 445.7 367.1 251 294.7 510.4 1100 230-384 427.8 216.8 2257 Freezing Data Freezing Point, °C -77.7 - 189.3 5.5 -17.4 -138.5 -56.6 -114.2 -156 -10.8 18.9 -259.2 - 160 -24.9 NOT FOR DIS -97.7 -210 -57.5 -218.8 -187.7 -96.6 0.0 Latent Heat of Fusion Temperature, Density hif, kJ/kg °C p, kg/m³ 322.4 28 126 80.3 109 108 181.1 200.6 59.5 105.7 11.4 58.4 99.2 25.3 180.7 13.7 80.0 333.7 -33.3 -20 0 25 -185.6 20 20 -0.5 0 25 20 20 20 -268.9 -252.8 -11.7 20 25 -161.5 -100 25 -195.8 - 160 20 25 - 183 20 -42.1 0 50 -50 -26.1 0 25 0 25 Liquid Properties 50 75 00 682 665 639 602 1394 879 1150 601 298 783 789 1109 1261 146.2 70.7 593.8 820 13,560 423 301 787 809 596 703 910 1141 640 581 529 449 1443 1374 1295 1207 1000 997 988 975 958 Specific Heat Cp, kJ/kg.K 4.43 4.52 4.60 4.80 1.14 1.72 3.11 2.31 0.59 2.46 2.84 2.84 2.32 22.8 10.0 2.28 2.00 0.139 3.49 5.79 2.55 2.06 2.97 2.10 1.80 1.71 2.0 2.25 2.53 3.13 1.23 1.27 1.34 1.43 4.22 4.18 4.18 4.19 4.22
Properties of saturated water Temp. T, °C 0.01 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 110 120 130 140 150 160 170 180 190 200 220 240 260 280 300 320 340 360 Enthalpy Specific of Heat Density p, kg/m³ Thermal Conductivity k, W/m.K Vaporization C, J/kg.K Liquid Vapor Liquid Vapor Liquid 9.593 4190 1936 1948 971.8 0.2935 2309 hig, kJ/kg Liquid Vapor 0.6113 999.8 0.0048 2501 4217 1854 0.561 0.0171 1.792 x 10-3 0.8721 999.9 0.0068 2490 4205 1857 0.571 0.0173 1.519 x 10-3 1.2276 999.7 0.0094 2478 4194 1862 0.580 0.0176 1.307 x 10-3 1.7051 999.1 0.0128 2466 4185 1863 0.589 0.0179 1.138 x 10-³ 2.339 998.0 0.0173 2454 4182 1867 0.598 0.0182 1.002 x 10-³ 3.169 997.0 0.0231 2442 4180 1870 0.607 0.0186 0.891 x 10-³ 4.246 996.0 0.0304 2431 4178 1875 0.615 0.0189 0.798 x 10-³ 5.628 994.0 0.0397 2419 4178 1880 0.623 0.0192 0.720 x 10-³ 7.384 992.1 0.0512 2407 4179 1885 0.631 0.0196 0.653 x 10-3 990.1 0.0655 2395 4180 1892 0.637 0.0200 0.596 x 10-³ 988.1 0.0831 2383 4181 1900 0.644 0.0204 0.547 x 10-3 985.2 0.1045 2371 4183 1908 0.649 0.0208 0.504 x 10-3 983.3 0.1304 2359 4185 1916 0.654 0.0212 0.467 x 10-³ 980.4 0.1614 2346 4187 1926 0.659 0.0216 0.433 x 10-3 977.5 0.1983 2334 0.663 0.0221 0.404 x 10-3 974.7 0.2421 2321 4193 0.667 0.0225 0.378 x 10-3 4197 1962 0.670 0.0230 0.355 x 10-³ 968.1 0.3536 2296 4201 1977 0.673 0.0235 0.333 x 10-³ 965.3 0.4235 2283 4206 1993 0.675 0.0240 0.315 x 10-3 961.5 0.5045 2270 4212 2010 0.677 0.0246 0.297 x 10-³ 957.9 0.5978 2257 4217 2029 0.679 0.0251 0.282 x 10-3 950.6 0.8263 2230 4229 2071 0.682 0.0262 0.255 x 10-3 2203 4244 2120 0.683 0.0275 0.232 x 10-³ 2174 4263 2177 0.684 0.0288 0.213 x 10-3 2145 4286 2244 0.683 0.0301 0.197 X 10-³ 2114 4311 2314 0.682 0.0316 0.183 x 10-3 2083 4340 2420 0.680 0.0331 0.170 x 10-³ 2050 4370 2490 0.677 0.0347 0.160 x 10-³ 2015 4410 2590 0.673 0.0364 0.150 x 10-³ 1979 4460 2710 0.669 0.0382 0.142 x 10-³ 1941 4500 2840 0.663 0.0401 0.134 x 10-³ 1859 4610 3110 0.650 0.0442 0.122 x 10-3 1767 4760 3520 0.632 0.0487 0.111 x 10-3 1663 4970 4070 0.609 0.0540 0.102 x 10-³ 1544 5280 4835 0.581 0.0605 0.094 x 10-3 1405 5750 5980 0.548 0.0695 0.086 x 10-3 1239 6540 7900 0.509 0.0836 0.078 x 10-³ 1028 8240 11,870 0.469 0.110 0.070 x 10-3 720 14,690 25,800 0.427 0.178 0.060 x 10-3 0 0.043 x 10-3 943.4 1.121 934.6 1.496 921.7 1.965 916.6 2.546 907.4 3.256 897.7 4.119 887.3 5.153 876.4 6.388 864.3 7.852 840.3 11.60 813.7 16.73 783.7 23.69 750.8 33.15 713.8 46.15 667.1 64.57 610.5 92.62 528.3 144.0 317.0 317.0 Saturation Pressure Psat kPa 12.35 15.76 19.94 25.03 31.19 38.58 47.39 57.83 70.14 84.55 101.33 143.27 198.53 270.1 361.3 475.8 617.8 791.7 1,002.1 1,254.4 1,553.8 2,318 3,344 4,688 6,412 8,581 11,274 14,586 18,651 374.14 22,090 Dynamic Viscosity μ, kg/m-s Prandtl Number Pr Vapor Liquid Vapor 0.922 x 10-5 0.934 x 10-5 0.946 x 10-5 13.5 11.2 9.45 8.09 7.01 6.14 5.42 1.00 1.00 1.00 1.00 1.00 0.959 x 10-5 0.973 x 10-5 0.987 x 10-5 1.001 x 10-5 1.016 x 10-5 1.031 x 10-5 1.046 x 10-5 1.062 x 10-5 1.077 x 10-5 1.093 x 10-5 1.110 x 10-5 1.126 x 10-5 1.142 x 10-5 1.159 x 10-5 1.176 x 10-5 1.193 x 10-5 1.210 x 10-5 1.227 x 10-5 1.261 x 10-5 1.296 x 10-5 4.83 1.00 4.32 1.00 3.91 1.00 3.55 1.00 3.25 1.00 2.99 1.00 2.75 1.00 2.55 1.00 2.38 1.00 2.22 1.00 2.08 1.00 1.96 1.00 1.85 1.75 1.58 1.00 1.00 1.00 1.00 1.330 x 10-5 1.44 1.33 1.24 1.01 1.02 1.365 x 10-5 1.399 x 10-5 1.434 x 10-5 1.16 1.02 1.05 1.09 1.468 x 10-5 1.03 1.05 1.502 x 10-5 0.983 1.07 1.537 x 10-5 0.947 1.09 1.571 x 10-5 0.910 1.11 1.641 x 10-5 0.865 1.15 1.712 x 10-5 0.836 1.24 1.788 x 10-5 0.832 1.35 1.870 x 10-5 0.854 1.965 x 10-5 0.902 2.084 x 10-5 2.255 x 10-5 2.571 x 10-5 4.313 x 10-5 1.49 1.69 1.97 2.43 3.73 1.00 1.23 2.06 Volume Expansion Coefficient B, 1/K Liquid 1.00 -0.068 x 10-3 1.00 0.015 x 10-3 0.733 x 10-3 0.138 x 10-3 0.195 x 10-3 0.247 x 10-3 0.294 x 10-3 0.337 x 10-3 0.377 x 10-3 0.415 x 10-3 0.451 x 10-3 0.484 x 10-3 0.517 x 10-3 0.548 x 10-3 0.578 x 10-³ 0.607 x 10-³ 0.653 x 10-3 0.670 x 10-3 0.702 x 10-³ 0.716 x 10-3 0.750 x 10-³ 0.798 x 10-3 0.858 x 10-3 0.913 x 10-3 0.970 x 10-³ 1.025 x 10-³ 1.145 x 10-3 1.178 x 10-3 1.210 x 10-³ 1.280 x 10-3 1.350 x 10-3 1.520 x 10-3 1.720 x 10-3 2.000 x 10-3 2.380 x 10-3 2.950 x 10-3 Note 1: Kinematic viscosity and thermal diffusivity a can be calculated from their definitions, p/p and a = k/pcp= = v/Pr. The temperatures 0.01°C, 100°C, and 374.14°C are the triple-, boiling-, and critical-point temperatures of water, respectively. The properties listed above (except the vapor density) can be used at any pressure with negligible error except at temperatures near the critical-point value.
Transcribed Image Text:Properties of saturated water Temp. T, °C 0.01 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 110 120 130 140 150 160 170 180 190 200 220 240 260 280 300 320 340 360 Enthalpy Specific of Heat Density p, kg/m³ Thermal Conductivity k, W/m.K Vaporization C, J/kg.K Liquid Vapor Liquid Vapor Liquid 9.593 4190 1936 1948 971.8 0.2935 2309 hig, kJ/kg Liquid Vapor 0.6113 999.8 0.0048 2501 4217 1854 0.561 0.0171 1.792 x 10-3 0.8721 999.9 0.0068 2490 4205 1857 0.571 0.0173 1.519 x 10-3 1.2276 999.7 0.0094 2478 4194 1862 0.580 0.0176 1.307 x 10-3 1.7051 999.1 0.0128 2466 4185 1863 0.589 0.0179 1.138 x 10-³ 2.339 998.0 0.0173 2454 4182 1867 0.598 0.0182 1.002 x 10-³ 3.169 997.0 0.0231 2442 4180 1870 0.607 0.0186 0.891 x 10-³ 4.246 996.0 0.0304 2431 4178 1875 0.615 0.0189 0.798 x 10-³ 5.628 994.0 0.0397 2419 4178 1880 0.623 0.0192 0.720 x 10-³ 7.384 992.1 0.0512 2407 4179 1885 0.631 0.0196 0.653 x 10-3 990.1 0.0655 2395 4180 1892 0.637 0.0200 0.596 x 10-³ 988.1 0.0831 2383 4181 1900 0.644 0.0204 0.547 x 10-3 985.2 0.1045 2371 4183 1908 0.649 0.0208 0.504 x 10-3 983.3 0.1304 2359 4185 1916 0.654 0.0212 0.467 x 10-³ 980.4 0.1614 2346 4187 1926 0.659 0.0216 0.433 x 10-3 977.5 0.1983 2334 0.663 0.0221 0.404 x 10-3 974.7 0.2421 2321 4193 0.667 0.0225 0.378 x 10-3 4197 1962 0.670 0.0230 0.355 x 10-³ 968.1 0.3536 2296 4201 1977 0.673 0.0235 0.333 x 10-³ 965.3 0.4235 2283 4206 1993 0.675 0.0240 0.315 x 10-3 961.5 0.5045 2270 4212 2010 0.677 0.0246 0.297 x 10-³ 957.9 0.5978 2257 4217 2029 0.679 0.0251 0.282 x 10-3 950.6 0.8263 2230 4229 2071 0.682 0.0262 0.255 x 10-3 2203 4244 2120 0.683 0.0275 0.232 x 10-³ 2174 4263 2177 0.684 0.0288 0.213 x 10-3 2145 4286 2244 0.683 0.0301 0.197 X 10-³ 2114 4311 2314 0.682 0.0316 0.183 x 10-3 2083 4340 2420 0.680 0.0331 0.170 x 10-³ 2050 4370 2490 0.677 0.0347 0.160 x 10-³ 2015 4410 2590 0.673 0.0364 0.150 x 10-³ 1979 4460 2710 0.669 0.0382 0.142 x 10-³ 1941 4500 2840 0.663 0.0401 0.134 x 10-³ 1859 4610 3110 0.650 0.0442 0.122 x 10-3 1767 4760 3520 0.632 0.0487 0.111 x 10-3 1663 4970 4070 0.609 0.0540 0.102 x 10-³ 1544 5280 4835 0.581 0.0605 0.094 x 10-3 1405 5750 5980 0.548 0.0695 0.086 x 10-3 1239 6540 7900 0.509 0.0836 0.078 x 10-³ 1028 8240 11,870 0.469 0.110 0.070 x 10-3 720 14,690 25,800 0.427 0.178 0.060 x 10-3 0 0.043 x 10-3 943.4 1.121 934.6 1.496 921.7 1.965 916.6 2.546 907.4 3.256 897.7 4.119 887.3 5.153 876.4 6.388 864.3 7.852 840.3 11.60 813.7 16.73 783.7 23.69 750.8 33.15 713.8 46.15 667.1 64.57 610.5 92.62 528.3 144.0 317.0 317.0 Saturation Pressure Psat kPa 12.35 15.76 19.94 25.03 31.19 38.58 47.39 57.83 70.14 84.55 101.33 143.27 198.53 270.1 361.3 475.8 617.8 791.7 1,002.1 1,254.4 1,553.8 2,318 3,344 4,688 6,412 8,581 11,274 14,586 18,651 374.14 22,090 Dynamic Viscosity μ, kg/m-s Prandtl Number Pr Vapor Liquid Vapor 0.922 x 10-5 0.934 x 10-5 0.946 x 10-5 13.5 11.2 9.45 8.09 7.01 6.14 5.42 1.00 1.00 1.00 1.00 1.00 0.959 x 10-5 0.973 x 10-5 0.987 x 10-5 1.001 x 10-5 1.016 x 10-5 1.031 x 10-5 1.046 x 10-5 1.062 x 10-5 1.077 x 10-5 1.093 x 10-5 1.110 x 10-5 1.126 x 10-5 1.142 x 10-5 1.159 x 10-5 1.176 x 10-5 1.193 x 10-5 1.210 x 10-5 1.227 x 10-5 1.261 x 10-5 1.296 x 10-5 4.83 1.00 4.32 1.00 3.91 1.00 3.55 1.00 3.25 1.00 2.99 1.00 2.75 1.00 2.55 1.00 2.38 1.00 2.22 1.00 2.08 1.00 1.96 1.00 1.85 1.75 1.58 1.00 1.00 1.00 1.00 1.330 x 10-5 1.44 1.33 1.24 1.01 1.02 1.365 x 10-5 1.399 x 10-5 1.434 x 10-5 1.16 1.02 1.05 1.09 1.468 x 10-5 1.03 1.05 1.502 x 10-5 0.983 1.07 1.537 x 10-5 0.947 1.09 1.571 x 10-5 0.910 1.11 1.641 x 10-5 0.865 1.15 1.712 x 10-5 0.836 1.24 1.788 x 10-5 0.832 1.35 1.870 x 10-5 0.854 1.965 x 10-5 0.902 2.084 x 10-5 2.255 x 10-5 2.571 x 10-5 4.313 x 10-5 1.49 1.69 1.97 2.43 3.73 1.00 1.23 2.06 Volume Expansion Coefficient B, 1/K Liquid 1.00 -0.068 x 10-3 1.00 0.015 x 10-3 0.733 x 10-3 0.138 x 10-3 0.195 x 10-3 0.247 x 10-3 0.294 x 10-3 0.337 x 10-3 0.377 x 10-3 0.415 x 10-3 0.451 x 10-3 0.484 x 10-3 0.517 x 10-3 0.548 x 10-3 0.578 x 10-³ 0.607 x 10-³ 0.653 x 10-3 0.670 x 10-3 0.702 x 10-³ 0.716 x 10-3 0.750 x 10-³ 0.798 x 10-3 0.858 x 10-3 0.913 x 10-3 0.970 x 10-³ 1.025 x 10-³ 1.145 x 10-3 1.178 x 10-3 1.210 x 10-³ 1.280 x 10-3 1.350 x 10-3 1.520 x 10-3 1.720 x 10-3 2.000 x 10-3 2.380 x 10-3 2.950 x 10-3 Note 1: Kinematic viscosity and thermal diffusivity a can be calculated from their definitions, p/p and a = k/pcp= = v/Pr. The temperatures 0.01°C, 100°C, and 374.14°C are the triple-, boiling-, and critical-point temperatures of water, respectively. The properties listed above (except the vapor density) can be used at any pressure with negligible error except at temperatures near the critical-point value.
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