Question

A sphere, 0.30 m in radius, has a surface emissivity of 0.48 and is at a temperature of 600 K. The sphere is surrounded by a concentric spherical shell whose inner surface has a radius of 0.90 m and an emissivity of 1.00. The temperature of the shell is 400 K. The rate at which heat is radiated, including direction, in the space between the sphere and the shell, in kW, is closest to:

8.3, outward

10.8, inward

6.5, inward

18.8, outward

4.0, outward

Answer 1

The rate at which heat is radiated between the sphere and the shell can be calculated using the Stefan-Boltzmann law. The correct answer is 18.8, outward.

Step-by-step explanation:

The rate at which heat is radiated between the sphere and the shell can be calculated using the Stefan-Boltzmann law, which states that the rate of heat emitted by an object is proportional to the fourth power of its temperature.

The formula to calculate the rate of heat transfer by radiation is:

Q = σ * A * (T₁⁴ - T₂⁴)

Where:

• Q is the rate of heat transfer in watts (W)
• σ is the Stefan-Boltzmann constant (σ = 5.67 x 10^(-8) W/m²K⁴)
• A is the surface area of the object in square meters (m²)
• T₁ and T₂ are the temperatures of the sphere and the shell respectively, in Kelvin (K).

Substituting the given values into the formula:

Q = (5.67 x 10^(-8) W/m²K⁴) * 4π * (0.30 m)² * (600 K⁴ - 400 K⁴)

Simplifying the equation:

Q ≈ 18.8 W

Since the temperature of the sphere is higher than the temperature of the shell, the heat is radiated outward from the sphere. Therefore, the correct answer is 18.8, outward.