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**Cycles Contributions by:**

John L. Falconer & Will Medlin Department of Chemical and Biological Engineering University of Colorado Boulder, CO Supported by the National Science Foundation

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**Consider the best possible heat engine working in air at 25°C**

Consider the best possible heat engine working in air at 25°C. The engine continuously converts heat from a source at 300°C to work, and heat is continuously transferred into the engine at a rate of 100 kJ/s. The maximum possible rate at which the engine can continuously produce work is ___________ 100 kJ/s. greater than equal to almost significantly less than ANSWER: D. significantly less than 100 kJ/s. The second law says heat cannot be converted all into work continuously. Heat has to be rejected to the surroundings, so significantly less than 100 kJ/s of work will be obtained. The best that can be attained, through an ideal Carnot cycle, is less than 50%.

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**For a Carnot heat engine, which statement must be incorrect?**

|Qc| > |W| |QH| < |W| |QH| > |QC| ANSWER: B. QH < W. Second law says that the maximum work out of an engine is the amount of heat added at high temperature.

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**Is this consistent with the 1st and 2nd laws?**

A Carnot heat engine is run in reverse so for every 100 kJ of electrical work added to the pump, 700 kJ of heat is added to the building. Is this consistent with the 1st and 2nd laws? Yes No Cannot be determined ANSWER: A. Yes. It is possible to get more heat out than work added.

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Which diagram corresponds to a Carnot engine in which both adiabatic steps in the cycle are irreversible? T S 1 2 4 3 A B T S 1 2 4 3 D S T 1 2 4 3 T S 1 2 4 3 C ANSWER: C. The entropy must increase for the two adiabatic, irreversible steps.

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Which diagram corresponds to a Carnot heat pump in which both adiabatic steps in the cycle are irreversible? T S 1 4 2 3 T S 1 4 2 3 A B T S 1 4 3 T S 1 4 2 3 ANSWER: A. A Carnot heat pump must run counter clockwise on a T-S diagram and entropy must increase for the two adiabatic, irreversible steps. C D

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**A B C D Which diagram represents a Rankine cycle? P P H H P P H H**

ANSWER: C. Starting from the bottom left corner, the pump increases the pressure on the liquid while slightly increasing the enthalpy, the boiler operates at constant pressure and vaporizes that liquid, the turbine decreases the pressure and enthalpy since work is done, and the condenser condenses the vapor at constant pressure. P P H H

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**A B C D E Which diagram represents a Rankine cycle? P P P H H H P P H**

ANSWER: C. Either this one or the previous one should be deleted. P P H H

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**Which diagrams are not possible for a vapor compression refrigeration cycle using a throttle valve?**

#1 #2 #3 S S S 2 & 5 1 & 4 2, 3, & 4 1, 2, 4, & 5 1, 4, & 5 T T #4 #5 ANSWER: A. 2 & 5. Diagram #2 shows no entropy change through the throttle, but the entropy must increase as the saturated liquid becomes liquid and vapor through the throttle. Diagram #5 shows an entropy decrease during the gas compression step, but reversible entropy change must be zero. The refrigerant is starting as a saturated vapor and is compressed to a superheated vapor and would not decrease as shown in this diagram. S S

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**Which diagrams do not represent a vapor compression cycle**

Which diagrams do not represent a vapor compression cycle? The compressor is adiabatic, the expansion valve is a throttle process, the evaporator and condenser are each at constant pressure. P P P #1 #2 #3 ANSWER: B. 1 & 2 do not represent vapor compression cycles. Diagram #1 shows no enthalpy change through the compressor and there must be an increase in enthalpy as work is done on the fluid during compression. Diagram #2 shows a decreasing pressure in the condenser step and the problem states it should be constant. H H H 1 1 & 2 2 2 & 3 3

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**Which diagrams do not represent a vapor compression cycle**

Which diagrams do not represent a vapor compression cycle? The compressor is adiabatic, the expansion valve is a throttle process, the evaporator and condenser are each at constant pressure. P P P #1 #2 #3 H H H ANSWER: C Diagrams 1 & 3 do not represent vapor compression cycles. Diagram #1 shows an increase in enthalpy during the expansion valve step. Because the expansion valve is a throttle process, the change in enthalpy must be zero. Diagram #3 shows a decrease in pressure during the evaporator step and the evaporator should be at constant pressure. 1 1 & 2 1 & 3 2 & 3 3

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Indicate, in the correct order, which P-H diagram represents a vapor compression cycle and which represents a Rankine power cycle. 1& 2 2 & 3 3 & 4 4 & 2 1 & 3 P P #1 #2 H H ANSWER: D. P P #3 #4 H H

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**Which line is most likely to represent a reversible turbine in a Rankine cycle?**

D Pressure Enthalpy (kJ/kg) ANSWER: C. The inlet to the turbine should be superheated steam and the exit must have lower enthalpy than the inlet since work is done by the turbine.

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**C A D B Which line is most likely to represent a liquid pump? Pressure**

Enthalpy (kJ/kg) ANSWER: C. Liquid pump does not add much energy, but it does add some so enthalpy increases.

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**A well-insulated water heater heats water from 10°C to 50°C. **

The efficiency of the process is _______________ . much greater than 1 much less than 1 almost equal to 1 not possible to tell ANSWER: C. almost equal to 1. The well-insulated water heater can convert essentially all the electrical work into heat.

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**Which will require more work to compress from 1 atm to 100 atm?**

Liquid Gas Solid ANSWER: B. Gas. There is a much larger volume change when compressing the gas, so there is much more work done.

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**What can you definitely say about this system?**

Liquid water at 1.5 MPa and 180°C expands continuously through a throttling valve to 100 kPa. What can you definitely say about this system? All the liquid evaporates Some of the liquid evaporates The temperature increases The temperature does not change ANSWER: B. Some of the liquid evaporates. The enthalpy change associated with decompressing water to 100 kPa and its saturation temperature at that pressure (100 C) is less than the enthalpy of vaporization of water at atmospheric pressure. See steam tables.

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**What can you definitely say about this system?**

Liquid water at 1.5 MPa and 180°C expands continuously through a throttling valve to 100 kPa. What can you definitely say about this system? All the liquid evaporates The temperature increases The temperature decreases The temperature does not change ANSWER: C. The temperature decreases. As some of the water evaporates at the outlet, the evaporation requires energy so the temperature decreases.

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**1,000 J/s electrical energy is supplied to a heat pump for a house**

1,000 J/s electrical energy is supplied to a heat pump for a house. Which is the most likely amount of heat that is provided to the house? 35,000 J/s 3,000 J/s 1,000 J/s 400 J/s ANSWER: B. 3,000 J/s. More heat is generated than work input to a heat pump, but not 35 times more.

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**Rank the following types of energy in terms of quality: **

1) hot combustion gas 2) hot water 3) electricity 4) chemical energy 4 > 3 > 1 > 2 3 > 4 > 1 > 2 3 > 1 > 4 > 2 4 > 1 > 3 > 2 4 > 3 > 2 > 1 ANSWER: B. 3 > 4 > 1 > 2

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The quality of steam from an irreversible turbine, compared to a reversible turbine, at the same final pressure is _______. higher lower the same ANSWER: A. higher. Since less useable work is removed from an irreversible turbine to the same final pressure as a reversible turbine, the temperature is greater at the outlet of an irreversible turbine. Quality is the mass fraction of vapor.

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**The efficiency of this process is ____________ 100%.**

Liquid water at 10°C flows into an insulated tank where an electric heating element heats it to its exit temperature of 50°C. The efficiency of this process is ____________ 100%. much greater than about equal to much less than Answer: B. about equal to 100%. Almost all the electrical work can be converted to heat (small lose through walls of tank if insulated).

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**Which cannot be done continuously?**

Convert 100 kJ work to 100 kJ heat Convert 100 kJ electricity to 200 kJ heat Convert 100 kJ heat to 100 kJ work Both A and B ANSWER: C. Convert 100 kJ heat to 100 kJ work. This violates the second law to continuously convert heat completely to work. Note that (B) requires additional source of heat to complete energy balance.

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**Which statement is incorrect?**

Work can be continuously converted to heat with efficiency close to 100% Heat can be continuously converted to work with efficiency close to 80% Electricity can be continuously converted to work with efficiency greater than 50% Electricity can be converted to heat with efficiency close to 100% ANSWER: B. Heat can be continuously converted to work with efficiency close to 80%

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**Suppose both adiabatic steps in a Carnot cycle are irreversible**

Suppose both adiabatic steps in a Carnot cycle are irreversible. Which is the correct statement about the entropy change of the Carnot engine? ΔSengine > 0 ΔSengine = 0 ΔSengine < 0 None of the above ANSWER: B. Delta S(engine) = 0. The engine still runs in a cycle and returns to the starting point, so there is no entropy change because S is a state function. However, the entropy generation in the surroundings will be higher.

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