Topic: Heat Transfer
A radiator in a domestic heating system operates at a surface temperature of 55°C. Assuming the radiator behaves as a black body, the rate at which it emits the radiant heat per unit area is (assume $\sigma = 5.67 \times 10^{-8} \text{ W}/(\text{m}^2\text{K}^4)$)
- A. 0.66 kW/m²
- B. 0.0005 kW/m²
- C. 0.5 kW/m²
- D. 66 kW/m²
Answer: A. 0.66 kW/m²
Explanation: For a black body, the emissivity $\epsilon$ is 1. The rate of radiant heat emission per unit area is defined by the Stefan-Boltzmann law: $Q/A = \sigma T^4$. First, convert the temperature to Kelvin: $T = 55 + 273 = 328 \text{ K}$. Substituting the values yields $Q/A = 1 \times 5.67 \times 10^{-8} \times (328)^4 = 656.26 \text{ W/m}^2$, which is approximately 0.66 kW/m².