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Chemical Engineering Basics - Engineering

Q1:

In a counter flow heat exchanger, hot fluid enters at 170°C & leaves at 150°C, while the cold fluid enters at 50°C & leaves at 70°C. The arithmetic mean temperature difference in this case is __________ °C.

A 20

B 60

C 120

D ∞

ANS:D - ∞

The arithmetic mean temperature difference (ΔTm) in a counterflow heat exchanger can be calculated using the formula: ΔTm=ln(ΔT2ΔT1​)/(ΔT1−ΔT2)​ Where:

  • ΔT1 = Temperature difference of the hot fluid = (T1in - T1out)
  • ΔT2 = Temperature difference of the cold fluid = (T2in - T2out)
Given: Hot fluid:
  • T1in = 170°C
  • T1out = 150°C Cold fluid:
  • T2in = 50°C
  • T2out = 70°C
Calculating ΔT1 and ΔT2: ΔT1=(170°C−150°C)=20°C ΔT2=(70°C−50°C)=20°C Now, substituting the values into the formula: ΔTm=ln(20°C20°C​)(20°C−20°C)​ Since the numerator is 0, and the natural logarithm of 1 is 0, the expression becomes indeterminate (0/0), which implies that the arithmetic mean temperature difference is undefined in this case. So, the correct answer is ∞ (undefined).