Discussion
Saturated vapour is condensed to saturated liquid in a condenser. The heat capacity ratio is \(C_{r} = \frac{C_{min}}{C_{max}}\). The effectiveness (∈) of the condenser is :
Answer: A
The effectiveness is \(1 - \exp(-\text{NTU})\).
In a condenser the condensing vapour stays at its saturation temperature while it gives up latent heat, so its effective heat capacity rate is infinite. That makes \(C_{max} \to \infty\), and so the capacity ratio \(C_{r} = C_{min}/C_{max} = 0\).
Putting \(C_{r} = 0\) in any of the standard effectiveness relations, parallel or counter flow, gives the same result:
\[ \varepsilon = 1 - e^{-\text{NTU}} \]
Option B is the parallel-flow relation, which reduces to this only when \(C_{r} = 0\); option C is a garbled counter-flow form; and \(\frac{\text{NTU}}{1 + \text{NTU}}\) is the counter-flow result for \(C_{r} = 1\), the opposite limit.
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