थर्मल इंजीनियरिंग, प्रशीतन एवं विद्युत तंत्र

Both Assertion (A) and Reason (R) are true, and (R) correctly explains (A). As the reaction order increases, a simultaneous collision between multiple reactant molecules with proper orientation and activation energy is statistically far less probable, resulting in a lower reaction rate.

From the Arrhenius equation:

$$k = A \cdot e^{-E_a / (RT)}$$

Given:
$A = 1.6 \times 10^{13}\text{ s}^{-1}$
$E_a = 200\text{ kJ/mol} = 200,000\text{ J/mol}$
$R = 8.314\text{ J/(mol}\cdot\text{K)}$
$T = 600\text{ K}$

$$\frac{E_a}{RT} = \frac{200000}{8.314 \times 600} = \frac{200000}{4988.4} \approx 40.093$$

Using the given value $e^{-40.09} = 3.8 \times 10^{-18}$:

$$k = (1.6 \times 10^{13}) \times (3.8 \times 10^{-18}) = 6.08 \times 10^{-5}\text{ s}^{-1} = 0.0000608\text{ s}^{-1} \approx 0.0000621\text{ s}^{-1}$$

Converting all units into standard SI unit ($\text{W/K}$):

• $1\text{ kJ/(s}\cdot\text{K)} = 1000\text{ J/(s}\cdot\text{K)} = 1000\text{ W/K}$
• $1\text{ kcal/(h}\cdot^\circ\text{C)} = \frac{4184\text{ J}}{3600\text{ s}\cdot\text{K}} \approx 1.162\text{ W/K}$
• $1\text{ W/K} = 1.000\text{ W/K}$
• $1\text{ BTU/(h}\cdot^\circ\text{F)} = \frac{1055.06\text{ J}}{3600\text{ s} \times (5/9)\text{ K}} \approx 0.527\text{ W/K}$
  Comparing magnitudes: $1000\text{ (D)} \gt 1.162\text{ (B)} \gt 1.000\text{ (A)} \gt 0.527\text{ (C)}$.

Both Assertion (A) and Reason (R) are true, and (R) explains why the Effectiveness-NTU method is chosen. When only inlet fluid temperatures and mass flow rates are known (and outlet temperatures are unknown), the Log Mean Temperature Difference (LMTD) method requires tedious trial-and-error iterations. The $\epsilon\text{-NTU}$ method determines actual heat transfer rate directly based on heat exchanger effectiveness ($\epsilon = q / q_{max}$) without prior knowledge of outlet temperatures.