HW 7B-2: Rate of Entropy Increase for a Heat Transfer Process

LearnThermo.com Homework Problem 7B-2

A hot reservoir at 944 K transfers heat to a cold reservoir at 298 K. If the rate of heat transfer is 25 kW,determine the rate at which the entropy of the two reservoirs combined changes (in kW/K) and determine if the second law is satisfied.

For hints and answers visit:
http://www.LearnThermo.com/T1-tutorial/ch07/lesson-B/pg20.php#P2

HW 7B-1: Entropy Change for a Heat Transfer Process

LearnThermo.com Homework Problem 7B-1

Calculate the entropy change of each reservoir when 1000 kJ of heat is transferred directly from a hot reservoir at 1000 K to a cold reservoir at 400 K. Calculate the entropy change of the universe for this process. Does this process violate the principle of increasing entropy?

For hints and answers visit:
http://www.LearnThermo.com/T1-tutorial/ch07/lesson-B/pg20.php#P1

TE 303 - Please give Dr.B some feedback about Thermo-CD

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TE 303 - HW #8, P1 - Inventor Claim for Silicon Chip - 20 pts

An inventor claims to have created a silicon chip whose surface temperature is no more than 60 °C. The silicon chip has dimensions of 5 mm on each side with a 1 mm thickness, and is embedded in a ceramic substrate. At steady state, the chip has an electrical power input of 0.225 W. The top surface of the chip is exposed to a coolant whose temperature is 20 °C. The heat transfer coefficient for convection (h) between the coolant and chip is 105 W/m²•K. Evaluate the inventor's claim using the following:

a.) First Law Energy Balance, assuming that the heat transfer by conduction between the chip and substrate is negligible.

b.) Second Law Energy Balance: Calculate entropy generation.

In your analysis section, be sure to comment on what is the main source of entropy generation in this system.

No old comments.

TE 303 - HW #8, P2 - Maximum Work From an Adiabatic Turbine - 10 pts

Steam enters an adiabatic turbine at 800 psia and 900^oF and leaves at a pressure of 40 psia. Determine the maximum amount of work that can be delivered by this turbine.

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TE 303 - HW #8, P3 - Lost Work in a Heat Exchanger - 15 pts

A well-insulated shell-and-tube heat exchanger is used to heat water (CP = 4.18 kJ/kg-K) in the tubes from 20oC to 70oC at a rate of 4.5 kg/s. Heat is supplied by hot oil (CP = 2.30 kJ/kg-K) that enters the shell side at 170oC at a rate of 10 kg/s.



Disregarding any heat loss from the heat exchanger, determine...

a.) The exit temperature of the oil.
b.) The rate of entropy generation in the heat exchanger.
c.) The rate at which work is lost due to the irreversible nature of heat transfer in this process in kW. Assume the surroundings are at 20oC.

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TE 303 - HW #8, P4 - Entropy Generation and Lost Work in a Nozzle - 20 pts

Oxygen, O2, enters a nozzle operating at steady-state at 3.8 MPa, 387oC and 10 m/s. At the nozzle exit, the conditions are 150 kPa, 37oC and 790 m/s.

a.) For a system that encloses the nozzle only, determine the heat transfer (kJ/kg) and the change in specific entropy (kJ/kg-K), both per kg of oxygen flowing through the nozzle. What additional information would be required to evaluate the rate of entropy production in this process ?

b.) Using an enlarged system boundary that includes the nozzle and a portion of its immediate surroundings, evaluate the rate of entropy generation (kJ/kg-K) and the rate of lost work (kJ/kg), both per kg of oxygen flowing through the nozzle. Assume that heat exchange at the enlarged system boundary takes place at the ambient temperature, 20oC.

Treat O2 as an ideal gas with variable heat capacities. Verify that the ideal gas assumption is valid.

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TE 303 - HW #8, P5 - Entropy Balance for a Power Plant - 25 pts

The figure to the right shows a simple vapor power plant operating at steady state with water as the working fluid. Data at key locations are given in the figure. The mass flow rate of the water circulating through the components is 109 kg/s. Stray heat transfer and kinetic and potential energy effects can be ignored.



Determine the following:

a.) The mass flow rate of the cooling water, in kg/s.
b.) The thermal efficiency.
c.) The rates of entropy production, each in kW/K, for the turbine, condenser, and pump.

In your analysis section, place the components in rank order, beginning with the component contributing most to inefficient operation of the overall system.

No old comments.

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 ?

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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.

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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.

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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.

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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.

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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.

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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