# Entropy Change in Heat Exchange of Liquids

A heat exchanger uses 5000 kg/hr of water to cool hydrocarbon oil from 140oC to 65oC. The oil, flowing at the rate of 2500 kg/hr has an average specific heat of 0.6 kcal/kg.oC. The water enters at 20oC. Determine

1. The entropy change of the oil
2. Entropy change of water
3. The total entropy change as a result of this heat exchange process.

Calculations:

By energy balance, moilCPoilDToil = mwaterCPwaterDTwater

DTwater = 2500 x 0.6 x (140 - 65) / (5000 x 1) = 22.5oC

Therefore, exit temperature of water = 20 + 22.5 = 42.5oC

Entropy change is given by

DS = mCP ln (T2/T1)

where m is mass flow rate of stream, T1 and T2 are respectively initial and final temperatures.

(i) Entropy change of oil:

T1 = 140 + 273 = 413 K

T2 = 65 + 273 = 338 K

Mass flow rate of oil = 2500 kg/hr = 0.6944 kg/sec

DSoil = 0.6944 x 0.6 x ln (338/413) = -0.0835 kcal/sec.oC

(ii) Entropy change of water:

T1 = 20 + 273 = 293 K

T2 = 42.5 + 273 = 315.5 K

Mass flow rate of water = 5000 kg/hr = 1.389 kg/sec

DSwater = 1.389 x 1 x ln (315.5/293) = 0.1028 kcal/sec.oC

(iii) Total entropy change:

Total entropy change is the sum of the entropy changes of two streams, and = -0.0835 + 0.1028 = 0.0193 kcal/sec.oC