An adiabatic heat exchanger is used to heat cold water at 15°C entering at a rate of 5 kg/s by hot air at 90°C entering also at rate of 5 kg/s. If the exit temperature of hot air is 20°C, the exit temperature of cold water is

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  1. 27°C
  2. 32°C
  3. 52°C
  4. 85°C

Answer (Detailed Solution Below)

Option 2 : 32°C
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Detailed Solution

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Concept:

By usimg equilibrium of heat exchanger, we know that,

Heat loss by Hot air = Heat gain by cold water

\({\left( {m{C_p}\Delta T} \right)_{Air}} = {\left( {m{C_p}\Delta T} \right)_{water}}\)

Calculation:

Given:

For air:

Ti = 90°C, To = 20°C, m = 5 kg/s, Cp = 1 kJ/kgK

For water:

Ti = 15°C, To = ?,  m = 5 kg/s, Cp = 4.2 kJ/kgK

⇒ 5 × 1 × (90 – 20) = 5 × 4.2 × (Tf – 15)

Tf = 31.6° C
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