CHAPTER 11 PROBLEMS

K. CHAPTER 11 PROBLEMS

Problem K1 Is the reaction expression written on a molecular basis the same as the mole basis?

Problem K2 Under what condition is the A: F ratio based on a mole basis the same as the volume basis?

Problem K3 Consider propane gas C 3 H 8 , which can be empirically written as CH 2.6667 . The stoichiometric air: fuel ratio per kmol of C 3 H 8 is exactly equal to the stoichiometric air per kmol of CH 2.6667 . True or False?

Problem K4 For an adiabatic reaction, one can reasonably assume that the entropy of products leaving is the same as entropy of the reactants. True or False?

Problem K5 For an adiabatic reaction involving PCW, one can reasonably assume that the en- thalpy of products is the same as the enthalpy of the reactants. True or False?

Problem K6 For an adiabatic reaction within a closed system, the entropy increases at fixed values U,V, m. True or False?

Problem K7 In an adiabatic reaction within a PCW, the entropy increases at fixed H, P, m. True or False?

Problem K8 During a CO 2 sequestration process, the reaction CaO(s) + CO2 (g) → CaCO3(s) oc- curs. How much heat in kJ/kmol of CO 2 is required for the reaction at 298 K?

Problem K9 Currently at a 370 ppm level of CO 2 in the ambient, about 7 billion metric tons of carbon is emitted every year. which is expected to rise to 1 gigatons by 2015 and 4 gigatons by 2025. If the dominant fuel used is coal CH 0.7589 O 0.1816 N 0.0128 S 0.00267 , how much fuel can be burned each year to reach these levels?

Problem K10 About 90% of the CO 2 emitted dissolves into the oceans and forms a methane hydrate sediment through the reaction CO 2 + bH 2 O → CH 4 : 7H 2 O(s) + CO 2 . How much CO 2

is captured by 1 kmol of H 2 O?

Problem K11

A glass jar that contains N moles of dry air is placed in a pool of water. A combusti- ble solid, CH m O n is ignited and dropped into the jar. A lid is snugly fitted at the neck of the jar. Sometimes the lid is seen to fall into the jar. (a) Determine the appropriate conditions for this to occur. Discuss the problem for (i) m = 1, n = 0, (ii) m = 0, n = 0

(pure carbon). (b) What are the results if CO is formed instead of CO 2 ? Will the lid be expelled away from the jar?

Problem K12 At 25ºC and 1 bar is the reaction 4Fe(s) + 3O 2 → 2Fe 2 O 3 (s) exothermic?

Problem K13 The dry ash free cattle waste can be represented as CH 1.253 N 0.0745 O 0.516 S 0.00813 . The heating value of dry waste with 53% ash is known to be as 9215 kJ/kg . Determine a) stoichiometric air fuel ratio for a dry ash free fuel, b) enthalpy of formation in kJ/kmol for the empirical fuel, and c) adiabatic flame temperature in K for a dry fuel with 53% ash. Assume that c p of ash = 0.800 kJ/kg K.

Problem K14 In a HiTAC (high temperature air combustion) process the air is mixed with flue gases in order to reduce O 2 concentration to 2-5%. If methane is used with a stoichiometric ratio of 2 with 2% oxygen concentration in the oxidant stream (air + flue gas mixture), and air temperatures are a) 298 K, b) 1000 K, then determine the adiabatic flame temperatures. Assume constant specific heats for all species.

Problem K15 As opposed to burning glucose ( s f = 212 kJ/kmol), the body burns a mixture of fat (palmitic acid, C 16 H 32 O 2 , h f = - 834694.4 kJ/kmol, s f = 452.37 kJ/kmol) and glucose. Let the heat loss rate be specified at 110 W for 70 kg person and breathing rate at 0.1 liter per second. Determine the entropy generation per kmol of the mixture vs. the fraction of glucose in the fuel metabolized and entropy generation per unit amount metabolism. Comment on the results. What happens to the results if the fat is replaced

by cholesterol C 27 H 45 OH? Assume that cholesterol has the same properties as fat. Problem K16

The human body is an open system and some arbitrary person, on average, loses body heat at the rate of 110 W. Assume that person’s body temperature remains constant at

37ºC, the ambient temperature is 25ºC, the specific heat of air is 1 kJ kg –1 K , the in- halation (and exhalation) mass flow rates are both 6 g min –1 and properties of exhaled

gas are the same as that of air. Determine the entropy generation rate: a)

If the control volume is assumed just inside the human body.

b) If the control volume is assumed just outside of the human body. Explain the difference between answers in (a) or (b)

Problem K17 Normally for closed system: dS = dH / T - VdP / T or dU / T + PdV / T . Con- sider a closed system which is suddenly loaded with 1 K mole of CO and 1 K mole of

O 2 at 3000 K. a) What are the entropy and enthalpy at this (meta) state (1). b) If you leave the system for a sufficiently long period of time and at the same time maintain the pressure at 1 atm and temperature at 3000 K, you find that there are 0.34 CO, 0.66

CO 2 and 0.67 oxygen moles (state 2). What is the entropy and enthalpy at state (2). c) What is the entropy change (S 2 - S 1 )? d) What is the enthalpy change? e) Is the en-

tropy change equal to ∆H/T where ∆H=H 2 -H 1 ? Comment.

Problem K18 Consider the growth of leaves on a tree. Consider a single leaf as it is growing. The gaseous CO 2 and liquid water are used to produce a solid leaf which is assumed to be cellulose C 6 H 10 O 5 . a) Develop an overall reaction scheme. The sunlight is used as an energy source for such a reaction. b) Write down the mass, energy and entropy bal- ance equations. Assume that reactions occur at 25ºC, 1 bar ? Determine a) sunlight required in kJ/kg of cellulose, b) entropy change for the reaction in kJ/kg K, c) repeat

parts (a) and (b) if the solid is lignin (C 40 H 44 O 6 ), and d) If wood consists of 40-45% cellulose, 15-30% lignin and the rest is hemi-cellulose, how will you determine the answers for (a) and (b)?

Problem K19 The body burns a mixture of glucose (C 6 H 12 O 6 ,h f0 = -1260268 kJ/kmol, s(298,s)=212 kJ/kmol K, HHV 2815832 kJ/kmol,10034905.6 kJ/kmol and fat (C 16 H 32 O 2 , h f = - 834694.4, s(298,s) =452 kJ/kmol K, HHV = 10034905.6 kJ/kmol K. If inhaled air temperature is 25ºC, and exhaled air temperature is 37ºC . Plot entropy generation in kJ per kmol of mixture K and in kJ per kJ of heat released per K vs. glucose fraction in the mixture. Assume 400% excess air.

Problem K20 Natural gas has the following composition based on molal%: CH 4 : 91.27, Ethane

2 3.78, N = 2.81, Propane 0.74, CO 2 : 0.68, n-Butane: 0.15, i-Butane 0.1, He 0.08, i pentane 0.05, n-pentane 0.04, H2: 0.02, C-6 and heavier (assume the species to be of

mole wt: 72): 0.26, Ar: 0.02. Determine a) the molecular weight, b) gross heating

value in BTU/SCF, kJ/m 3 , c) LHV.

Problem K21

a) In a constant volume combustion chamber one kmol of CH 4 and 3 kmol of O 2 are burned at 298 K and 1 bar. Heat Q v is removed so that the products are at 298 K a) What is the final pressure? Assume that H 2 O does not condense. b) If the same reac- tion involving the same molar content occurs in a sssf reactor at 298 K and 1 bar and the products leave at 298 K and 1 bar, the heat removed is Q p . c) Determine the dif-

ference (if any) between Q p and Q v . d) If H 2 O partially condenses, what is the value of Q P for case (b), e) If water partially condenses, what is the value of Q V and the fi- nal pressure?

Problem K22 CH 4 was supplied to a reactor along with air. The dry gas analysis yields the follow- ing composition CO 2 : 4%, O 2 : 7%. a) Determine the CO content in the products, b) A:

F, c) equivalence ratio, and d) air required in m 3 /hr for combustion of 15 m 3 /hr of fuel at STP.

Problem K23 Gaseous CO 2 and liquid water are used to produce a hydrocarbon during photosynthe- sis that leads to leaf growth. Sunlight is used as the energy source for the reaction.

Describe the mass, energy and entropy balance equations for this process. It is argued that the leaf is formed by groups of organized molecules while CO 2 is disorganized and as such order increases and hence the entropy may decrease. Is this a violation of Second Law?

Problem K24 Octane C 8 H 18 is burned with dry air at P = 14.7 psia. a) Calculate stoichiometric A: F ratio. If volumetric analyses of dry products are CO 2 : 7%, O 2 : 10.90%, N 2 : 82.10%, then determine b) equivalence ratio for actual combustion and c) dew point tempera- ture of H 2 O in the products.