TE 303 - HW #7, P1 - The Increase of Entropy - 15 pts

a.) Will the entropy of steam increase, decrease or remain the same as it flows through a real adiabatic turbine ?

b.) Will the entropy of the working fluid in an ideal Carnot Cycle increase, decrease or remain the same during the isothermal heat addition process ?

c.) Steam is accelerated as it flows through a real, adiabatic nozzle. Will the entropy of the steam at the nozzle exit be greater than, equal to or less than the entropy at the nozzle inlet ?

3 old comments

TE 303 - HW #7, P2 - Efficiency of an Int. Rev. HE with Multiple Heat Transfers - 10 pts

A system executes a power cycle while receiving 750 kJ by heat transfer at 1500 K and rejecting 100 kJ of heat at 500 K. A heat transfer from the system also occurs at 1000 K. There are no other heat transfers. If no internal irreversibilities exist in this system, determine the thermal efficiency of this cycle.

No old comments.

TE 303 - HW #7, P3 - ΔSSys, ΔSRes, and ΔSUniv, for a H.T. Process - 15 pts

During the isothermal heat addition process of a Carnot Cycle, 900 kJ of heat is added to the working fluid from a source at 400oC. Determine:

a.) the entropy change of the working fluid
b.) the entropy change of the heat source
c.) the total entropy change of the universe for this process.

1 old comment

TE 303 - HW #7, P4 - Specific Entropy Change Using Tabluar Data - 16 pts

Using the appropriate table, determine the change in specific entropy in kJ/kg-K for:

a.) Water: P1 = 10 MPa, T1 = 400 degC and P2 = 10 MPa, T2 = 100 degC.
b.) R-134a: H1 = 211.44 kJ/kg, T1 = - 40 degC and P2 = 5 bar, x2 = 1.0.
c.) Air (IG): T1 = 7 degC, P1 = 2 bar and T2 = 327 degC, P2 = 1 bar.
d.) Hydrogen (H2, IG): T1 = 727 degC, P1 = 1 bar and T2 = 25 degC, P2 = 3 bar.

4 old comments

TE 303 - HW #7, P5 - DSUniv Upon Quenching an Iron Block - 20 pts

A 12 kg iron block initially at 350 degC is quenched in an insulated tank that contains 100 kg of water at 22 degC. Assuming the water that vaporizes during the process condenses back into the liquid phase inside the tank, determine the entropy change of the universe for this process.

6 old comments

TE 303 - HW #7, P6 - DS for Heat Transfer to R-134a in a Rigid Tank - 18 pts

A 0.5 m3 rigid tank contains R-134a initially at 200 kPa and 40% quality. Heat is transferred to the refrigerant from a source at 35oC until the pressure rises to 400 kPa. Determine…

a.) The entropy change of the R-134a.
b.) The entropy change of the heat source.
c.) The entropy change of the universe for this process.

2 old comments

TE 303 - HW #6, P1 - "Show That" Using the K-P Statement of the 2nd Law - 10 pts

Using the Kelvin-Planck statement of the 2nd Law, demonstrate the following corollaries.

a.) The coefficient of performance (COP) of an irreversible heat pump cycle is always less than the COP of a reversible heat pump when both heat pumps exchange heat with the same two thermal reservoirs.

b.) All reversible heat pump cycles exchanging heat with the same two thermal reservoirs have the same COP.

8 Old Comments

TE 303 - HW #6, P2 - Rev., Irrev. and Impossible Refrigeration Cycles - 16 pts

A refrigeration cycle operating between two reservoirs receives QC from a cold reservoir at TC = 250 K and rejects QH to a hot reservoir at TH = 300 K. For each of the following cases, determine whether the cycle is reversible, irreversible or impossible.

a.) QC = 1000 kJ and Wcycle = 400 kJ
b.) QC = 1500 kJ and QH = 1800 kJ
c.) QH = 1500 kJ and Wcycle = 200 kJ
d.) COP = 4

No Old Comments.

TE 303 - HW #6, P3 - A Reversible HE Used to Drive a Reversible Heat Pump - 10 pts

A reversible power cycle receives QH from a reservoir at TH and rejects QC to a reservoir at TC. The work developed by the power cycle is used to drive a reversible heat pump that removes Q'C from a reservoir at T'C and rejects Q'H to a reservoir at T'H.

a.) Develop an expression for the ratio Q'H / QH in terms of the temperatures of the four reservoirs.
b.) What must be the relationship of the temperatures TH, TC, T'C and T'H for Q'H / QH to exceed a value of 1.0 ?

9 Old Comments

TE 303 - HW #6, P4 - COMPUTER ANALYSIS: Temp Effects on HE Efficiency - 15 pts

A heat engine operates between a source at TH and a sink at TC. Heat is supplied to the heat engine at a steady rate of 1200 kJ/min. Study the effects of TH and TC on the maximum power produced and the maximum cycle efficiency. For TC = 25oC, let TH vary from 300oC to 1000oC. Create plots of Wcycle and ηth as functions of TH. For TH = 550oC, let TC vary from 0oC to 50oC. Create plots of Wcycle and ηth as functions of TC. Discuss the results. Please note that there will be NO credit given for this problem if it is not solved with Excel.

6 Old Comments

TE 303 - HW #6, P5 - Maximum Efficiency of an OTEC Power Plant - 8 pts

Ocean temperature energy conversion (OTEC) power plants generate power by utilizing the naturally occurring decrease with depth of the temperature ocean water. Near Florida, the ocean surface temperature is 27oC while at a depth of 700 m the temperature is 7oC. Determine the maximum possible thermal efficiency for any power cycle operating between these two temperatures. The thermal efficiency of existing OTEC plants is approximately 2%, so compare this value with your result. In your analysis section (4 pts), also comment on whether you think that OTEC power plants are viable alternatives to existing power plants.

No Old Comments.

TE 303 - HW #6, P6 - Carnot Gas Power Cycle Analysis - 16 pts

One kg of air as an ideal gas executes a Carnot power cycle having a thermal efficiency of 60%. The heat transfer to the air during the isothermal expansion is 40 kJ. At the end of the isothermal expansion, the pressure is 5.6 bar and the volume is 0.3 m3. Determine...

a.) The maximum and mininmum temperatures for the cycle in Kelvin.
b.) The pressure in bar and volume in m3 at the beginning of the isothermal expansion.
c.) The work and heat transfer for each of the four processes in kJ.
Assume: CV,air = 0.731 kJ/kg-K(constant).
d.) Sketch the cycle on a PV diagram.

9 Old Comments

TE 303 - HW #6, P7 - Carnot HE Used to Drive a Carnot Refrigerator - 10 pts

A Carnot Heat Engine receives heat from a reservoir at 900oC at a rate of 800 kJ/min and rejects the waste heat to the ambient air at 27oC. The entire work output of the heat engine is used to drive a refrigerator that removes heat from the refrigerated space at -5oC and rejects heat to the same ambient air at 27oC. Determine:

a.) the maximum rate of heat removal from the refrigerated space
b.) the total rate of heat rejection to the ambient air

No Old Comments

TE 303 - HW #6, P8 - Ammonia Carnot Vapor Refrigeration Cycle - 15 pts

Three kg of ammonia executes a Carnot vapor refrigeration cycle. During the isothermal compression (cooling) step, the ammonia begins as a saturated mixture at 10 bar with a quality of 97% and it is cooled until it is a saturated liquid. The adiabatic compression step requires 128 kJ/kg of work to increase the pressure from 1.1 bar to 10 bar.

a.) Sketch the cycle on a PV diagram.
b.) Evaluate the heat and work for each process in kJ.
c.) Evaluate the COP for this cycle.

7 Old Comments