(i) CalculateDS of the two gas streams for countercurrent flow
(ii) What isDStotal?
(iii) If heating stream enters at 200oC, what isDStotal?
Basis: 1 mole of gas
Entropy change for the constant pressure heating/cooling process:
DS = nCP ln (T2/T1)
Where T1 and T2 are respectively initial and final temperatures.
(i) Entropy change of the cold gas stream:
T1 = 273 + 70 = 343 K
T2 = 273 + 190 = 463 K
n = 1
Therefore, DS = (7R/2) x ln (463/343) = 1.05 R
Entropy change of the Hot gas stream:
T1 = 273 + 320 = 593 K
Since the flow rates of the two streams are same,
DThotstream = DTcoldstream = 190 - 70 = 120 K
T2 = T1 - 120 = 593 - 120 = 473 K
n = 1
Therefore, DS = (7R/2) x ln (473/593) = -0.79 R
(ii) DStotal = 1.05 R + (-0.79R) = 0.26 R
(iii) Heating stream inlet temperature = 200oC
Therefore, outlet temperature of heating stream = 200 - 120 = 80oC
DS for this stream = (7R/2) x ln (353/473) = -1.024 R
DStotal = 1.05 R + (-1.024 R) = 0.026 R