Question Bank • QB_DFE_HMT_012 MCQ • 1 Mark

Section 7: Dairy and Food Engineering

Heat and Mass Transfer

Subtopic: Steady state heat transfer in conduction, convection and radiation

Question Statement:

Two large parallel black plates are maintained at absolute temperatures $T_1 = 400\text{ K}$ and $T_2 = 300\text{ K}$. With Stefan-Boltzmann constant $\sigma = 5.67 \times 10^{-8}\text{ W/(m}^2\cdot\text{K}^4)$, the net radiative heat flux between the plates ($q/A = \sigma(T_1^4 - T_2^4)$) is closest to:

Options:

  • (A) $\approx 992\text{ W/m}^2$
  • (B) $\approx 1450\text{ W/m}^2$
  • (C) $\approx 450\text{ W/m}^2$
  • (D) $\approx 2200\text{ W/m}^2$

Answer Key:

A

Step-by-Step Solution & Explanation

Using Stefan-Boltzmann's law for ideal blackbodies: $q/A = \sigma (T_1^4 - T_2^4) = 5.67 \times 10^{-8} \times (400^4 - 300^4)$ $400^4 = 2.56 \times 10^{10}, \quad 300^4 = 0.81 \times 10^{10}$ $\Delta = (2.56 - 0.81) \times 10^{10} = 1.75 \times 10^{10}\text{ K}^4$ $q/A = 5.67 \times 10^{-8} \times 1.75 \times 10^{10} = 5.67 \times 175 = 992.25\text{ W/m}^2 \approx 992\text{ W/m}^2$
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