Thermodynamics, Energy & Mechanics

The curved upper-left boundary of the psychrometric chart is the saturation curve, representing $100\%$ relative humidity ($\text{RH} = 100\%$), where dry bulb temperature, wet bulb temperature, and dew point temperature are all equal. Option analysis: (A) $100\%$ relative humidity defines the saturation curve. (B) $0\%$ relative humidity is the horizontal dry air base axis. (C) Wet bulb lines are diagonal straight lines intersecting the curve. (D) Humid volume lines are steep diagonal lines.

For a counter-flow heat exchanger, fluids flow in opposite directions:

• At End 1 (Hot fluid inlet & Cold fluid outlet):
  \[ \Delta T_1 = T_{h, \text{in}} - T_{c, \text{out}} = 22^\circ\text{C} - 3^\circ\text{C} = 19^\circ\text{C} \]
• At End 2 (Hot fluid outlet & Cold fluid inlet):
  \[ \Delta T_2 = T_{h, \text{out}} - T_{c, \text{in}} = 6^\circ\text{C} - (-2^\circ\text{C}) = 6 + 2 = 8^\circ\text{C} \]
• The Logarithmic Mean Temperature Difference (LMTD, \(\Delta T_m\)) is defined as: \[ \Delta T_m = \frac{\Delta T_1 - \Delta T_2}{\ln\left(\frac{\Delta T_1}{\Delta T_2}\right)} = \frac{19 - 8}{\ln\left(\frac{19}{8}\right)} \]

Detailed Analysis of Transport Phenomena Laws:

• Fourier's Law of Heat Conduction (B): Heat flux is directly proportional to temperature gradient: $q = -k \frac{dT}{dx}$. (Gradient-based).
• Newton's Law of Cooling (C): Convective heat transfer is driven by the temperature difference/gradient across the thermal boundary layer: $q = h(T_s - T_\infty) = -k_f \left(\frac{\partial T}{\partial y}\right)_{y=0}$. (Gradient-based).
• Fick's Law of Mass Diffusion (D): Mass flux is directly proportional to concentration gradient: $J = -D \frac{dC}{dx}$. (Gradient-based).
• Stefan-Boltzmann Law (A): Governs thermal radiation based on absolute temperature to the fourth power: $E = \epsilon \sigma T^4$. It depends on absolute surface temperature, not a spatial gradient.