A student calculates that the total heat transfer from a...

A student calculates that the total heat transfer from a spherical copper ball of diameter 18 cm initially at $200^{\circ} \mathrm{C}$ and its environment at a constant temperature of $25^{\circ} \mathrm{C}$ during the first 20 min of cooling is 3150 kJ . Is this result reasonable? Why?

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Key Concepts

Specific Heat Capacity

This concept refers to the amount of energy required to raise the temperature of a unit mass of a substance by one degree Celsius. It is critical in calculating the thermal energy stored or removed from an object when its temperature changes. In the context of cooling, the heat removed from an object is the product of its mass, specific heat capacity, and the temperature drop.

Thermal Energy Calculation

The principle of thermal energy calculation involves determining the total heat transfer by multiplying the mass of the object, its specific heat capacity, and the change in temperature. This approach helps verify if a computed value for heat transfer is reasonable by comparing it with the theoretical prediction based on the object's properties and temperature difference.

Geometric Calculations for Mass Estimation

For objects with regular shapes like a sphere, determining the mass often starts with calculating the volume using geometric formulas, then multiplying by the material’s density. For a sphere, the volume is given by (4/3)?r³. This mass is essential for computing the heat transfer using the specific heat capacity and temperature difference.

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