A 1000 L metal drum initially contains 80 kg of water at 30 degree C. The metal

Question

A 1000 L metal drum initially contains 80 kg of water at 30 degree C. The metal drum is to be filled with water by adding hot water (55 degree C) at 0.01 kg/s and superheated steam at 2.15 kg/hr, which is slow enough that all the steam condenses. The superheated steam is supplied at 250 degree C and 1 bar. Neglect all heat losses from the drum in this calculation. Given: density (liq water) = 1 g/cm^3. a) How long will it take for the tank to fill? (24.1 hr) b) Once the drum is full, what will be the final temperature of the water in the drum? (87 degree C) c) Determine the entropy generated for the process of filling the drum. (39.55 kJ/K)

Explanation / Answer

Mass of water that can be added to tank = 1000L *1Kg/L= 1000 kg

Tank already contains 80 kg of water. So water to be added= 1000-80 kg= 920 kg

Out of this 920 kg, 0.01 kg/s and flow rate of super heated steam=2.15 kg/hr

Since all the steam condenses, flow rate of combined stream= 0.01*3600 kg/hr ( 3600 sec=1hr)+2.15= 38.15 kg/hr

Time required for filling = 920/38.15= 24.15 hr

Super heated steam looses heat and this heat has to be gained by water at 30 deg.c and water at       55 deg.c. Let the final temperature of water= T

Water specific heat is assumed to be 4.184 Kj/Kg.K

Heat to be gained by water at 30 deg.c= mass* specific heat* temperature difference = 80*4.184*(T-30)= 335.72*(T-30) KJ/kg

Heat gained by hot water at 55 deg.c = 0.01*3600 kg/hr*24.15 *1000*4.184*(T-55)=3637.57*(T-55) Kj/Kg

Enthalpy of super heated steam at 250 deg.c and 1 bar ( from steam tables)= 2974.5 KJ/Kg. Its enthalpy when saturated at 1 bar pressure =419.1 Kj/Kg. Enthalpy change = (2974.5-419.1)* 2.15kg/hr*24.15 = 132683 Kj

Now the steam looses sensible heat from 100 deg.c to final temperatrue of T.

Hence 2.15*24.15*4.184*(100-T)

Total heat added= 132683+217*(100-T)= 3637.57*(T-55)+ 335.72*(T-30) KJ/kg

132683 +217*100-217T= 3637.57*T- 200066.4 +335.72T-10071.6

132683+21700 +200066.4+10071.6= T*(3637.57+335.72+217)

T= 87 deg.c

3. Entropy generation. Entropy gained by water at 30 deg.c= mCp* ln(T2/T1)

T2= 87+273= 360 K, T1= 30+273= 303 K, entropy gaiend = 80*4.184*ln(360/303)=58 Kj/K

Entropy gained by water at at 55 deg.c = 0.01*3600*24.15*4.184* ln (360/328)= 338 Kj/K

Entropyof saturated liquid at 1bar (100 deg.c) =1.3069Kj/kg ( from steam tables)

Entropy of super heated steam at 1 bar and 250 deg.c = 8.0342

Entropy change during condensation = (1.3069- 8.0342)* 2.15*24.15 Kj/K=-349 Kj/K

Entropy change of liquid water from 100 deg.c to 87 deg.c = 2.15*24.15*4.184*ln( 360/373)= -7.8 Kj/K

Total entrpy change of process= 58+338-349-7.8= 39.2 Kj/K

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