Refrigeration Engineering

Evaluating the Assertion and Reason concerning Horizontal silos:

The correct answer is Option 4: (A) is not correct but (R) is correct..

• Heat Transfer Area Calculation in Counterflow Exchanger:
• Heat Duty Absorbed by Water:

$$Q = \dot{m}_w C_{p,w} (T_{w,\text{out}} - T_{w,\text{in}}) = 3\text{ kg/s} \times 4,187\text{ J/(kg}\cdot\text{K)} \times (80 - 30)\text{ K} = 628,050\text{ W}$$

• Temperature Differences:

$$\Delta T_1 = T_{s,\text{in}} - T_{w,\text{out}} = 180^\circ\text{C} - 80^\circ\text{C} = 100^\circ\text{C}$$ $$\Delta T_2 = T_{s,\text{out}} - T_{w,\text{in}} = 130^\circ\text{C} - 30^\circ\text{C} = 100^\circ\text{C}$$ $$\text{LMTD} = \Delta T_1 = \Delta T_2 = 100^\circ\text{C} = 100\text{ K}$$

• Required Heat Transfer Surface Area ($A$):

$$A = \frac{Q}{U \times \text{LMTD}} = \frac{628,050\text{ W}}{820\text{ W/(m}^2\cdot\text{K)} \times 100\text{ K}} = 7.659\text{ m}^2 \approx 7.66\text{ m}^2$$

• Conclusion: 7.66 m² (Option 1).

Correct option: (1) 7.66 m?

• Arrangement of Physical Constants by Increasing Magnitude:
• Evaluating the numerical magnitude of each physical constant in standard SI units:
• Planck's Constant ($h$): $h \approx 6.626 \times 10^{-34}\ \text{J}\cdot\text{s}$ (Order of magnitude: $10^{-34}$)
• Stefan-Boltzmann Constant ($\sigma$): $\sigma \approx 5.670 \times 10^{-8}\ \text{W}\cdot\text{m}^{-2}\cdot\text{K}^{-4}$ (or $\text{kg}\cdot\text{s}^{-3}\cdot\text{K}^{-4}$, Order of magnitude: $10^{-8}$)
• Universal Gas Constant ($R$): $R \approx 8.314\ \text{J}\cdot\text{mol}^{-1}\cdot\text{K}^{-1}$ (Order of magnitude: $10^{0} \approx 8.31$)
• Speed of Light in Vacuum ($c$): $c \approx 2.998 \times 10^{8}\ \text{m/s}$ (Order of magnitude: $10^{8}$)
• Ranking by Numerical Value:

$$6.626 \times 10^{-34} \lt 5.670 \times 10^{-8} \lt 8.314 \lt 2.998 \times 10^{8}$$ $$\text{B} \lt \text{A} \lt \text{D} \lt \text{C}$$

• Conclusion: The increasing order of magnitude is B, A, D, C (Option 1).

Correct option: (1) B,A,D,C