A cube of material with emissivity of 0.4 is heated from room temperature of 20°C to 100°C.The net power radiated by the cube is 20 W.What is the volume of the cube? (σ = 5.6696 × 10^-8 W/m^2·K⁴ A)0.0014 m³ B)0.012 m³ C)0.11 m³ D)1.8 m³

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The net power radiated by a body according to the Stefan-Boltzmann law is given by $P = e\sigma A(T^4 - T_0^4)$, where $e$ is the emissivity, $\sigma$ is the Stefan-Boltzmann constant, $A$ is the surface area, $T$ is the temperature of the body, and $T_0$ is the ambient temperature. For a cube, $A = 6a^2$, where $a$ is the length of a side of the cube. Given $e = 0.4$, $\sigma = 5.6696 \times 10^{-8} \, \text{W/m}^2\text{K}^4$, $T = 100 + 273 = 373 \, \text{K}$, $T_0 = 20 + 273 = 293 \, \text{K}$, and $P = 20 \, \text{W}$, we can solve for $a$ and thus the volume $V = a^3$. Rearranging and solving for $a^3$ gives a volume close to the value in choice A.

A Cube of Material with Emissivity of 0