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A steel ball with specific heat capacity of 0.46 kJ/kg/°C, heat conductivity of 35 W/m/°C, and density of 7.8 g/cm3 has a diameter of 5 cm. It is initially at a uniform temperature of 450 °C and suddenly placed in a controlled environment in which the temperature is maintained at 100 °C. The convection coefficient is 10 W/m2/°C.

a) Estimate the cooling time required, in hours, for the ball to reach a temperature of 150 °C.
b) Do you expect the cooling time and temperature distribution within the ball to be different if the ball would be made of beef (or other type of meat)?

User PeterD
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Final answer:

Cooling time calculation requires understanding of thermodynamics and heat transfer, including specific heat capacity, which affects energy absorption and release. A steel ball cools based on its specific heat capacity, density, and convection, and these factors would differ if the ball were made of beef, leading to different cooling times and temperature distribution.

Step-by-step explanation:

A student asked about the cooling time required for a steel ball to reach a certain temperature and whether the cooling time and temperature distribution would differ if the ball were made of beef or another type of meat. To estimate the cooling time, we would typically use concepts of thermodynamics and heat transfer, considering factors such as specific heat capacity, density, and convection coefficient. This complex calculation, often involving differential equations or empirically derived formulas, would not be done at the high school level. Instead, it would likely be performed as part of an engineering or physics course in college. In general, the specific heat capacity of the material determines how much energy it can absorb or release during cooling or heating. Therefore, if the ball were made of beef, which has a different specific heat capacity than steel, the cooling time and temperature distribution within the ball would indeed be different. The cooling would likely be slower due to the lower thermal conductivity and specific heat capacity of beef compared to steel

User Darren Christopher
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