CHAPTER 13 PROBLEMS

M. CHAPTER 13 PROBLEMS

Unless otherwise stated assume the ambient temperature and pressure to be 298 K and 1 bar. Problem M1

In an adiabatic reaction, one can reasonably assume that the availability of products leaving an sssf reactor is the same as availability of the reactants. True or False?

Problem M2 In an adiabatic reaction within a PCW, one can reasonably assume that the availabil- ity of products is the same as availability of the reactants. True or False?

Problem M3

The fuel availability is independent of environmental conditions. True or False?

Problem M4 If you know the heating value of cattle manure as 5000 Btu/lb, can you determine the fuel availability?

Problem M5 Methane is burned with 40% of excess air isobarically at 1 atm. Methane and air enter the combustor fully mixed at 77ºF. What is the absolute stream availability unmixed reactants? What is the irreversibility due to adiabatic mixing, and adiabatic combus- tion? What is the absolute stream availability if the product temperature is 800ºR?

Problem M6 Octane at 298 K and 4 bar and air at 710 K and 4 bar enter an adiabatic reactor. Reac- tion products leave the reactor at 10 K and 4 bar. Determine the A: F ratio, the maximum possible sssf work, assuming the ambient temperature to be 298 K, and the entropy generated.

Problem M7 In an open system determine the adiabatic irreversibilities of (a) methanol, and (b) gasoline (i.e., CH 2.6 with a lower heating value of 47720 kJ kg –1 ) under stoichiometric conditions. Express your answers in terms of fractional heating values. (c) Which of the two fuels displays a larger irreversibility? (d) Do the values change if a closed system is considered? (e) Which fuel will you recommend for an automobile engine?

Assume that entropy of CH 2.6 is same as entropy of octane on unit mass basis Problem M8

One kmol of CO and 1/2 kmol of O 2 react at 0 K in an isothermal reactor. (a) What is the entropy of the reactants and products? . (b) Since σ ≥ 0, what is the heat transfer Q

at 0 K ? (c) Since Q = ∆H = H P –H R , what are the value of H P and H R , at 0 K?

Problem M9

A four stroke diesel engine has a 80.26 mm bore, and 88.9 mm stroke, and runs at 2400 RPM with 20% excess air. The fuel is approximated by the chemical formula

C 14 H 24.9 with a heating value of 42940 kJ kg –1 . a) How much power can be developed if the cycle efficiency is 40%? b) If instead of drawing air at 100 kPa and 300 K, tur- bocharged air is provided during the suction stroke at 300 kPa and 330 K, how much additional power is developed? Assume the same cycle efficiency as case (a). c) If the radiator takes in half of the heat rejected for case (a), what will be the exhaust tem- perature and hence what would have been the maximum possible power for case (a)?

Problem M10 In an open system determine the adiabatic irreversibilities of (a) methanol, and (b) gasoline (i.e., CH 2.6 with a lower heating value of 47720 kJ kg –1 ). Express your an- swers in terms of fractional heating values. (c) Which of the two fuels displays a larger irreversibility? (d) Do the values change if a closed system is considered? (e) Which fuel will you recommend for an automobile engine?

Problem M11 In a water gas shift reactor ( CO+ H 2 O → CO 2 +H2) each of the reactant species

enter at 298 K and 1 bar. The products leave at 1000 K and 1 bar. Calculate the irre- enter at 298 K and 1 bar. The products leave at 1000 K and 1 bar. Calculate the irre-

298 K. Determine the minimum work required to dissociate 1 kmol of water at 298 K and 1 bar if (a) pure and separated hydrogen and oxygen are to be produced (each at 1 bar, 298 K), and (b) a stoichiometric mixture of oxygen and hydrogen is to be pro- duced.

Problem M13 Determine the maximum work deliverable by a fuel cell consuming 1 kmol of H 2 that

reacts at 25ºC and 1 atm to form H 2 O(liq).

Problem M14 Determine the availability of iso-octane fuel and verify the result with the value tabulated in Table A-27B

Problem M15

A kmol of CH 4 and a stoichiometric amount of O 2 enter a fuel cell at 1 bar, and 298K and produce CO 2 and H 2 O(liq) at 298K, and 1 bar. Calculate the change in availabil- ities between the inlet and exit and the maximum possible work.

Problem M16 For fuel cells using hydrocarbon fuels, the anodic reaction is

C x H y + 2x H

2 O → x CO 2 + (4x+y)H + (4x+y)e ,

and the cathodic reaction is

(x+y/4)O 2 + (4x+y)H + + (4x+y)e – → (2x+y/2)H 2 O.

The overall reaction can be represented as

C x H y + (x + y/4) O 2 → x CO 2 + y/2 H 2 O. Therefore, for a hydrocarbon fuel C x H y , the electrons generated per molecule are rep-

resented by the relation (4x+y). a) If methane fuel is used in a fuel cell determine the maximum possible voltage. b) What will be the answers for octane fuel?

Problem M17 Determine the fuel availability for octane. Assume that T o = 298 K, p O 2 ,o = 0.2055,

p CO 2 ,o =0.003, and p HO 2 ,o = 0.0188. Determine the fuel availability in kJ/Kmol and the ratio of fuel availability to LHV. Problem M18 Hydrocarbon fuels are used to power submarine diesel engines. The exhaust passes

through a cooling system so that almost all the H 2 O in the products condenses and provides drinking water. The CO 2 left in the products is mixed with pure oxygen and fired back into the diesel engine. The intake gas is not air but a mixture of CO 2 and O 2 , such that the mole fraction of O 2 is 21%. Is the optimum work affected? Deter- mine the optimum work if a) air alone is used for burning the fuel, or b) the CO 2 and O 2 mixture is used for HC fuel. Assume that the reactants enter at 25ºC and 1 bar and the products leave at 25ºC and 1 bar with H 2 O in the liquid state. If ∆w opt =