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**Problem Statement:** One half of a kilogram of liquid water at 273 K (0 °C) is placed outside on a day when the temperature is 261 K (-12 °C). Assume that the heat is lost from the water only by means of radiation and that the emissivity of the radiating surface is 0.600. Consider two cases: 1. When the surface area of the water is (a) 0.035 m² (as it might be in a cup). 2. When the surface area of the water is (b) 1.5 m² (as it could be if the water were spilled out to form a thin sheet). For each case, (a) and (b), determine the time it takes the water to freeze into ice at 0 °C. **Input Fields:** - **(a) Number:** - Pre-filled with "154" - Units: Dropdown menu for selection - **(b) Number:** - Blank input field - Units: Dropdown menu for selection **Instructions:** To solve this problem, you will need to use principles of thermal radiation to calculate the time required for the water to freeze. Consider the Stefan-Boltzmann law, which states that the power radiated by a black body is proportional to the fourth power of its temperature. Use this information along with the given emissivity value to solve for the time in each scenario.
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Transcribed Image Text:**Problem Statement:** One half of a kilogram of liquid water at 273 K (0 °C) is placed outside on a day when the temperature is 261 K (-12 °C). Assume that the heat is lost from the water only by means of radiation and that the emissivity of the radiating surface is 0.600. Consider two cases: 1. When the surface area of the water is (a) 0.035 m² (as it might be in a cup). 2. When the surface area of the water is (b) 1.5 m² (as it could be if the water were spilled out to form a thin sheet). For each case, (a) and (b), determine the time it takes the water to freeze into ice at 0 °C. **Input Fields:** - **(a) Number:** - Pre-filled with "154" - Units: Dropdown menu for selection - **(b) Number:** - Blank input field - Units: Dropdown menu for selection **Instructions:** To solve this problem, you will need to use principles of thermal radiation to calculate the time required for the water to freeze. Consider the Stefan-Boltzmann law, which states that the power radiated by a black body is proportional to the fourth power of its temperature. Use this information along with the given emissivity value to solve for the time in each scenario.
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Step 3: Time it takes the water to freeze in case of B
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