Final answer:
This question deals with calculating the rate at which a sphere emits and absorbs thermal radiation using the Stefan-Boltzmann law, considering the sphere's radius, temperature, surrounding temperature, and emissivity.
Step-by-step explanation:
The question concerns the rate at which a sphere emits and absorbs thermal radiation, as well as its net rate of energy exchange, involving concepts from thermodynamics and specifically the sub-topic of radiation heat transfer. The calculations are based upon the Stefan-Boltzmann law, which states that the power radiated from a black body is proportional to the fourth power of its temperature, and its surface area.
Given the radius of the sphere, its temperature, the surrounding temperature, and its emissivity, one can calculate the rate of heat emission and heat absorption using the following formulas:
- Rate of heat emission (Pe) = ε⋅σ⋅A⋅T1^4
- Rate of heat absorption (Pa) = ε⋅σ⋅A⋅T2^4
Where ε is the emissivity, σ is the Stefan-Boltzmann constant (5.67 × 10−12 W/m2K4), A is the surface area of the sphere, T1 is the absolute temperature of the sphere, and T2 is the absolute temperature of the surrounding environment. To find the net rate of energy exchange, you subtract the absorption rate from the emission rate.
To solve the actual problem, you'd need to convert the temperatures from degrees Celsius to Kelvins by adding 273.15, calculate the surface area of the sphere with the formula A = 4πr2, and apply the Stefan-Boltzmann law.