Question 717: Thermodynamics & KTG

Question

Three identical metal spheres (of same surface area) have red, black and white colors and they are heated up to same temperature. They are allowed to cool. Arrange them from maximum rate of cooling to minimum rate of cooling

Accepted Answer

The cooling of each sphere is mainly due to radiation and is described by the StefanÃ¢ÂÂBoltzmann law:
$$P = \epsilon \sigma A (T^4 - T_{	ext{ambient}}^4)$$
where:
$$\epsilon$$ is the emissivity of the surface,
$$\sigma$$ is the StefanÃ¢ÂÂBoltzmann constant,
$$A$$ is the surface area,
$$T$$ is the temperature of the sphere,
$$T_{	ext{ambient}}$$ is the ambient temperature.
Since all spheres have the same surface area and are at the same temperature, the rate of cooling is directly proportional to their emissivities. Typically:
Black surfaces have high emissivity (close to 1),
Red surfaces generally have a moderate emissivity,
White surfaces tend to have low emissivity because they are more reflective.
Thus, the sphere with black color will radiate energy (and cool) the fastest, followed by the red sphere, while the white sphere cools the slowest.
Therefore, the order from maximum rate of cooling to minimum rate is:
Black
Red
White
This corresponds to Option A.

Answer

black, red, white

Answer

white, red, black,

Answer

red, black, white

Answer

red, white, black

Thermodynamics & KTG

Three identical metal spheres (of same surface area) have red, black and white colors and they are heated up to same temperature. They are allowed to cool. Arrange them from maximum rate of cooling to minimum rate of cooling

Choose the correct answer: