Answer
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Step 1: Understand the problem
The time it takes for water to freeze depends on various factors such as the initial temperature of the water, the container's material, and the surrounding temperature. However, in this case, we are given a specific temperature of 32 degrees Fahrenheit, which is the freezing point of water. Therefore, we will assume that the water is initially at a temperature above freezing and is placed in an environment where it can lose heat to reach the freezing point.
Step 2: Identify the relevant formula
Q/t = -kAΔT
The heat loss equation can be represented as: Where: - Q is the heat energy (in joules) - m is the mass (in kilograms) - c is the specific heat capacity (for water, it's approximately 4.18 J/g°C) - ΔT is the change in temperature (in degrees Celsius) We want to find the time (t), so we need to relate the heat loss equation to the cooling rate equation: Where: - k is the thermal conductivity (for water and air, it's approximately 0.023 W/mK) - A is the surface area (in square meters)
Final Answer
The time it takes for water to freeze at 32 degrees Fahrenheit (0 degrees Celsius) is given by the equation: t = \frac{-m}{kA}c Where: - m is the mass (in kilograms) - k is the thermal conductivity (for water and air, it's approximately 0.023 W/mK) - A is the surface area (in square meters) - c is the specific heat capacity (for water, it's approximately 4.18 J/g°C)
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